/* * Equations for the automorphism group stratification of the * coarse moduli space of genus 3 hyperelliptic curves (see [LR12]) * * [LR12] Lercier, R. and Ritzenthaler, C., Hyperelliptic curves and their * invariants: geometric, arithmetic and algorithmic aspects, * Journal of Algebra, Elsevier, 2012 * */ /*** * Relation of degree 5 satisfied by J8 --- Eq. (II) in Sec. 1.5 of [LR12] *********************************************$***************************/ A6 := (-2/27*J3^2+64/45*J6-8/45*J2*J4+1/405*J2^3); A7 := (1/30*J2*J5-2/5*J7+1/15*J3*J4); A8 := (-52/105*J4^2+2/15*J2*J6); A16 := 1/90*J3*J4^2*J5+1/36450*J2^4*J4^2-26/42525*J2^3*J4*J6-2/15*J5^2*J6-1/810*J2^2*J4^3-1/1215*J2*J3^2*J4^2+76/2835*J2*J4^2*J6+52/2835*J3^2*J4*J6-12/1225*J4^4+1/5*J4*J5*J7-1/30*J2*J7^2-2/15*J3*J6*J7+352/4725*J4*J6^2; B7 := (1/12*J3*J4-1/2*J7+1/24*J2*J5); B8 := (-1/12*J3*J5-8/135*J2*J6+1/540*J2^2*J4-1/9720*J2^4+2/105*J4^2+1/324*J2*J3^2); B9 := (-1/12*J2*J7-1/6*J3*J6); B17 := -1/2430*J2^3*J5*J6-17/315*J4*J6*J7-1/54*J3^2*J4*J7+1/81*J3^2*J5*J6+31/3780*J2*J4*J5*J6+1/972*J3^3*J4^2-1/29160*J2^3*J3*J4^2+1/1620*J2^3*J4*J7-1/2160*J2^2*J4^2*J5+1/180*J2^2*J6*J7+4/135*J5*J6^2+1/648*J2*J3*J4^3-1/140*J2*J4^2*J7+1/1134*J3*J4^2*J6+1/12*J3*J7^2; G := -4/5; C8 := (1/180*J2^2*J4-18/35*J4^2+1/12*J3*J5+2/15*J2*J6); C9 := (-1/180*J2^2*J5-1/4860*J2^3*J3+2/5*J4*J5-34/135*J3*J6+1/162*J3^3+1/270*J2*J3*J4); C10 := (-1/27*J3^2*J4+314/315*J4*J6-1/6*J3*J7-1/10*J2*J4^2+1/810*J2^3*J4-1/90*J2^2*J6); C18 := 3/35*J3*J4^2*J7+1/14580*J2^2*J3^2*J4^2+113/17010*J2^2*J4^2*J6-4/15*J5*J6*J7+17/42525*J2*J4*J6^2+1/90*J2*J3*J6*J7-4/32805*J2^3*J3^2*J6+26/3645*J2*J3^2*J4*J6-1/1080*J2*J3*J4^2*J5-1/437400*J2^5*J4^2+41/136080*J2^3*J4^3-11/437400*J2^3*J6^2-13/54675*J2^4*J4*J6-3/350*J2*J4^4+4/2187*J3^4*J6-1/168*J3^2*J4^3+1/180*J2^2*J7^2-8/245*J4^3*J6+40/243*J6^3-3/70*J3*J4*J5*J6+11/14580*J3^2*J6^2+1/492075*J2^6*J6; D9 := (-1/576*J2^2*J5-1/288*J2*J3*J4-1/6*J3*J6-1/16*J2*J7); D10 := (-3/32*J5^2+1/6480*J2^3*J4+11/210*J4*J6+13/1620*J2^2*J6+1/24*J3*J7+1/233280*J2^5-1/7776*J2^2*J3^2+1/288*J2*J3*J5+1/720*J2*J4^2-1/144*J3^2*J4); D11 := (1/18*J3*J4^2+1/144*J2*J3*J6+1/288*J2^2*J7+1/48*J2*J4*J5-1/48*J5*J6-5/16*J4*J7); D19 := 1/699840*J2^4*J3*J4^2+7/8640*J2*J5*J6^2-47/30240*J2^2*J4^2*J7-1/38880*J2^4*J4*J7+3/280*J4^2*J5*J6+1/81*J3^2*J6*J7-5/7776*J2^3*J6*J7-1/15552*J2^2*J3*J4^3-1/288*J2*J3*J7^2-29/30240*J2^2*J4*J5*J6+1/1296*J2*J3^2*J4*J7-1/648*J2*J3^2*J5*J6-85/27216*J2*J3*J4^2*J6+3/896*J2*J4^3*J5-1/23328*J2*J3^3*J4^2+1/19440*J2^4*J5*J6-1/51840*J2^3*J4^2*J5-1/486*J3^3*J4*J6+1/864*J3^2*J4^2*J5+83/90720*J3*J4*J6^2+1/72*J3*J5^2*J6+1/14580*J2^3*J3*J4*J6-1/2240*J3*J4^4+3/32*J5*J7^2-25/432*J6^2*J7-9/1120*J4^3*J7-67/15120*J2*J4*J6*J7-1/48*J3*J4*J5*J7; E := 1/30; E10 := (-3/32*J5^2-1/288*J2*J3*J5-1/8*J3*J7-19/432*J3^2*J4+1/810*J2^3*J4-11/144*J2*J4^2+661/630*J4*J6-1/90*J2^2*J6); E11 := (-1/6480*J2^2*J3*J4+13/810*J2*J3*J6+1/116640*J2^4*J3+1/4320*J2^3*J5+1/360*J2^2*J7+2/45*J3*J4^2-1/3888*J2*J3^3-1/4*J4*J7-1/60*J5*J6); E12 := (17/216*J2*J4*J6+1/24*J3*J4*J5+1/144*J2*J3*J7-27/80*J4^3-25/216*J6^2+25/648*J3^2*J6+1/270*J2^2*J4^2-1/1215*J2^3*J6+3/16*J5*J7); E20 := -1/19440*J2^3*J3*J4*J7+1/9720*J2^3*J3*J5*J6-1/7290*J2^2*J3^2*J4*J6+1/25920*J2^2*J3*J4^2*J5-1/2160*J2^2*J3*J6*J7-1/720*J2^2*J4*J5*J7-47/15120*J2*J3*J4^2*J7-1/720*J2*J5*J6*J7-331/3780*J3*J4*J6*J7+1/218700*J2^5*J4*J6+1/116640*J2^4*J4^3-377/907200*J2^2*J4^4-1/11664*J3^4*J4^2-1/144*J3^2*J7^2+19849/396900*J4^2*J6^2+1/349920*J2^3*J3^2*J4^2-83/127575*J2^3*J4^2*J6+83/1360800*J2^2*J4*J6^2+1/1080*J2^2*J5^2*J6-9/1400*J4^5-1/2592*J2*J3^2*J4^3+449/22680*J2*J4^3*J6+1/960*J2*J4^2*J5^2-1/48*J2*J4*J7^2+1/648*J3^3*J4*J7-1/324*J3^3*J5*J6+43/3240*J3^2*J4^2*J6+3/448*J3*J4^3*J5-29/15120*J2*J3*J4*J5*J6+7/4320*J3*J5*J6^2+9/70*J4^2*J5*J7-143/1680*J4*J5^2*J6; EQJ8 := J8^5 + (A8 + 2*B8 + C8) * J8^4 + (-A6*C10 - A7*B9 + 2*A8*B8 + A8*C8 + A16 + B7*B9*G + B7*G*D9 - B7*C9 + B8^2 + 2*B8*C8) * J8^3 + (-A6*B7*G*D11 - 2*A6*B8*C10 - A6*B9^2*G + A6*B9*C9 - A6*C18 + A7*B7*C10 - A7*B8*B9 - A7*B9*C8 - A7*B17 + A8*B7*B9*G + A8*B7*G*D9 - A8*B7*C9 + A8*B8^2 + 2*A8*B8*C8 + 2*A16*B8 + A16*C8 - B7^2*G*D10 + B7*B8*G*D9 - B7*B8*C9 + B7*B17*G + B8^2*C8) * J8^2 + (-A6*B7*B8*G*D11 + A6*B7*B9*G*D10 - A6*B7*G*D19 - A6*B8^2*C10 + A6*B8*B9*C9 - 2*A6*B8*C18 - 2*A6*B9*B17*G + A6*B17*C9 + A7*B7^2*G*D11 + A7*B7*B8*C10 - A7*B7*B9*G*D9 + A7*B7*C18 - A7*B8*B9*C8 - A7*B8*B17 - A7*B17*C8 - A8*B7^2*G*D10 + A8*B7*B8*G*D9 - A8*B7*B8*C9 + A8*B7*B17*G + A8*B8^2*C8 + A16*B7*B9*G + A16*B7*G*D9 - A16*B7*C9 + A16*B8^2 + 2*A16*B8*C8) * J8 + (- A6*B7*B8*G*D19 + A6*B7*B17*G*D10 - A6*B8^2*C18 + A6*B8*B17*C9 - A6*B17^2*G + A7*B7^2*G*D19 + A7*B7*B8*C18 - A7*B7*B17*G*D9 - A7*B8*B17*C8 - A16*B7^2*G*D10 + A16*B7*B8*G*D9 - A16*B7*B8*C9 + A16*B7*B17*G + A16*B8^2*C8); /*** * Discriminant Delta of degree 14 --- Eq. (III) in Sec. 1.5 of [LR12] *********************************************************************/ D14 := 369994358063104/492075*J2^7 - 364395343642624/10935*J2^5*J4 + 683055942467584/32805*J2^4*J3^2 - 10428636769288192/54675*J2^4*J6 - 163430755991552/1215*J2^3*J3*J5 + 773557223161856/1215*J2^3*J4^2 + 1930310469025792/405*J2^3*J8 + 16530764988416/243*J2^2*J3^2*J4 - 70934252748800/27*J2^2*J3*J7 + 3128790930685952/1215*J2^2*J4*J6 - 27296194379776/15*J2^2*J5^2 + 335549856481280/9*J2^2*J10 + 1727094849536/27*J2*J3^4 - 8473127331823616/3645*J2*J3^2*J6 + 6422633971712/9*J2*J3*J4*J5 - 138167587962880/9*J2*J3*J9 + 1328382667128832/675*J2*J4^3 + 2908427726618624/45*J2*J4*J8 - 89916875603968/5*J2*J5*J7 + 12048213670363136/1215*J2*J6^2 + 431773712384*J3^3*J5 + 27887955673088/81*J3^2*J4^2 + 5181284548608*J3^2*J8 - 469985685929984/45*J3*J4*J7 + 1257325050462208/135*J3*J5*J6 + 3773948974071808/675*J4^2*J6 + 884272562962432/15*J4*J10 - 221068140740608/5*J5*J9 - 55267035185152/9*J6*J8 - 215886856192*J7^2; /*** * C2xS4 stratum --- Eq. (9) in Sec. 3.2.1 of [LR12] ****************************************************/ C2S4Stratum := [ J10, J9, J8, J7, J6, J5, J4, 30*J3^2 - J2^3 ]; /* Explicit model */ fC2S4 := x^8 + 14*x^4 + 1; /*** * V8 stratum --- Eq. (10) in Sec. 3.2.1 of [LR12] *************************************************/ V8Stratum := [ 2520*J10 - J2^5, J9, 420*J8 + J2^4, J7, 36*J6 + J2^3, J5, 6*J4 - J2^2, J3 ]; /* Explicit model */ fV8 := x^8 - 1; /*** * U6 stratum --- Eq. (11) in Sec. 3.2.1 of [LR12] *************************************************/ U6Stratum := [ 430080*J10 + J2^5, J9, 17920*J8 - J2^4, J7, 2304*J6 + J2^3, J5, 96*J4 - J2^2, J3 ]; /* Explicit model */ fU6 := x*(x^6-1); /*** * C14 stratum --- Eq. (12) in Sec. 3.2.1 of [LR12] **************************************************/ C14Stratum := [ J10, J9, J8, J6, J5, J4, J3, J2 ]; /* Explicit model */ fC14 := x^7-1; /*** * C2xD8 stratum --- Eq. (XIII) in Sec. 3.2.2 of [LR12] ******************************************************/ C2D8Stratum := [ 630*J10 - 15*J4^2*J2 - 30*J4*J3^2 + J4*J2^3, 18*J9 - 2*J5*J2^2 + 15*J4*J3*J2 + 60*J3^3 - 2*J3*J2^3, 1260*J8 - 18*J4^2 - 63*J4*J2^2 - 420*J3^2*J2 + 14*J2^4, 3*J7 - J5*J2 + 3*J4*J3, 18*J6 - 9*J4*J2 - 60*J3^2 + 2*J2^3, 5*J5^2 - 6*J4^2*J2 - 30*J4*J3^2 + J4*J2^3, 3*J5*J4 - 2*J5*J2^2 + 15*J4*J3*J2 + 60*J3^3 - 2*J3*J2^3, 60*J5*J3 + 18*J4^2 - 15*J4*J2^2 - 60*J3^2*J2 + 2*J2^4, 54*J4^3 - 81*J4^2*J2^2 - 1080*J4*J3^2*J2 + 36*J4*J2^4 - 3600*J3^4 + 240*J3^2*J2^3 - 4*J2^6 ]; /* Explicit models If t = -1/72,2/3, then D14 = 0 If t = 0, then C2xS4 case If t = infinity, then V8 case */ fC2D8 := x^8 + 7/6*x^4 + 1/2*t + 1/144; /*** * D12 stratum --- Eq. (XIV) in Sec. 3.2.2 of [LR12] ***************************************************/ D12Stratum := [ 30240*J10 - 600*J4^2*J2 - 390*J4*J3^2 + 13*J4*J2^3, 3456*J9 - 24*J5*J2^2 - 120*J4*J3*J2 - 30*J3^3 + J3*J2^3, 60480*J8 - 14976*J4^2 + 504*J4*J2^2 + 210*J3^2*J2 - 7*J2^4, 12*J7 - J5*J2 - 2*J4*J3, 576*J6 - 72*J4*J2 - 30*J3^2 + J2^3, 180*J5^2 - 96*J4^2*J2 - 30*J4*J3^2 + J4*J2^3, 576*J5*J4 - 24*J5*J2^2 - 120*J4*J3*J2 - 30*J3^3 + J3*J2^3, 720*J5*J3 - 2304*J4^2 + 120*J4*J2^2 + 30*J3^2*J2 - J2^4, 55296*J4^3 - 5184*J4^2*J2^2 - 4320*J4*J3^2*J2 + 144*J4*J2^4 - 900*J3^4 + 60*J3^2*J2^3 - J2^6 ]; /* Explicit models If t = -1/486, -1/192, then D14 = 0 If t = 0, then C2xS4 case If t = infinity, then U6 case */ fC2D8 := x^7 - 7/9*x^4 + (-48*t - 8/81)*x; /*** * C2xC4 stratum --- Eq. (XV) in Sec. 3.2.2 of [LR12] *****************************************************/ C2C4Stratum := [ 2041200*J10 + 560520*J6*J4 + 2205*J6*J2^2 + 98091*J4^2*J2 - 5607*J4*J2^3 + 56*J2^5, J9, 85050*J8 + 13860*J6*J2 + 37908*J4^2 - 2961*J4*J2^2 + 28*J2^4, J7, 648000*J6^2 - 356400*J6*J4*J2 + 4275*J6*J2^3 - 839808*J4^3 + 75249*J4^2*J2^2 - 1449*J4*J2^4 + 8*J2^6, J5, J3 ]; /* Explicit models If t = 21/5, 168/5 then D14 = 0 If t = 24/5, then C2xS4 case If t = infinity, then V8 case */ fC2C4 := (x^4+2*x^2+5/147*t-1/7)*(x^4-5/147*t+1/7); /*** * C2^3 stratum --- Eq. (XVII) in Sec. 3.2.3 of [LR12] *****************************************************/ C2p3Stratum := [ 170100*J10 + 37890*J6*J4 - 22680*J5^2 + 4221*J4^2*J2 + 1680*J4*J3^2 - 56*J4*J2^3, 9720*J9 + 810*J7*J2 - 3330*J6*J3 - 2187*J5*J4 + 108*J5*J2^2 - 360*J4*J3*J2 - 240*J3^3 + 8*J3*J2^3, 85050*J8 - 11655*J6*J2 + 11340*J5*J3 + 2187*J4^2 - 1260*J4*J2^2 - 840*J3^2*J2 + 28*J2^4, 546750*J7^2 - 963900*J6*J4^2 + 453600*J6*J4*J2^2 + 1404000*J6*J3^2*J2 - 46800*J6*J2^4 + 320760*J5^2*J4 - 196830*J5^2*J2^2 + 204120*J5*J4*J3*J2 - 680400*J5*J3^3 + 22680*J5*J3*J2^3 - 12312*J4^3*J2 + 537570*J4^2*J3^2 + 32301*J4^2*J2^3 + 157680*J4*J3^2*J2^2 - 5256*J4*J2^5 + 82800*J3^4*J2 - 5520*J3^2*J2^4 + 92*J2^7, 145800*J7*J6 + 4050*J7*J2^3 - 64800*J6*J5*J2 + 83700*J6*J4*J3 - 16650*J6*J3*J2^2 + 77760*J5^2*J3 + 13122*J5*J4^2 - 5751*J5*J4*J2^2 + 8640*J5*J3^2*J2 + 252*J5*J2^4 - 10260*J4^2*J3*J2 + 2880*J4*J3^3 - 1896*J4*J3*J2^3 - 1200*J3^3*J2^2 + 40*J3*J2^5, 18225*J7*J5 + 7425*J6*J4*J2 + 43200*J6*J3^2 - 1440*J6*J2^3 - 10935*J5^2*J2 + 42525*J5*J4*J3 + 5103*J4^3 - 675*J4^2*J2^2 + 2250*J4*J3^2*J2 - 75*J4*J2^4 + 1800*J3^4 - 120*J3^2*J2^3 + 2*J2^6, 4860*J7*J4 - 810*J7*J2^2 - 1080*J6*J5 + 3330*J6*J3*J2 - 837*J5*J4*J2 - 2880*J5*J3^2 - 12*J5*J2^3 + 2916*J4^2*J3 + 360*J4*J3*J2^2 + 240*J3^3*J2 - 8*J3*J2^4, 12150*J7*J3 + 7560*J6*J4 - 1665*J6*J2^2 - 2430*J5^2 + 1620*J5*J3*J2 + 837*J4^2*J2 + 1530*J4*J3^2 - 231*J4*J2^3 - 120*J3^2*J2^2 + 4*J2^5, 32400*J6^2 + 28350*J6*J4*J2 + 87750*J6*J3^2 - 2925*J6*J2^3 - 21870*J5^2*J2 + 76545*J5*J4*J3 + 13122*J4^3 - 405*J4^2*J2^2 + 5130*J4*J3^2*J2 - 171*J4*J2^4 + 3600*J3^4 - 240*J3^2*J2^3 + 4*J2^6, 194400*J6*J5^2 + 2034720*J6*J4^2*J2 + 2073600*J6*J4*J3^2 - 777870*J6*J4*J2^3 - 2193750*J6*J3^2*J2^2 + 73125*J6*J2^5 - 913680*J5^2*J4*J2 + 518400*J5^2*J3^2 + 179550*J5^2*J2^3 + 1516320*J5*J4^2*J3 + 419175*J5*J4*J3*J2^2 + 1555200*J5*J3^3*J2 - 51840*J5*J3*J2^4 + 244944*J4^4 + 112590*J4^3*J2^2 - 1170720*J4^2*J3^2*J2 - 80451*J4^2*J2^4 + 86400*J4*J3^4 - 306810*J4*J3^2*J2^3 + 10131*J4*J2^6 - 147600*J3^4*J2^2 + 9840*J3^2*J2^5 - 164*J2^8, 22680*J6*J5*J4 - 4995*J6*J5*J2^2 - 14850*J6*J4*J3*J2 - 86400*J6*J3^3 + 2880*J6*J3*J2^3 - 7290*J5^3 + 26730*J5^2*J3*J2 + 2511*J5*J4^2*J2 - 80460*J5*J4*J3^2 - 693*J5*J4*J2^3 - 360*J5*J3^2*J2^2 + 12*J5*J2^5 - 10206*J4^3*J3 + 1350*J4^2*J3*J2^2 - 4500*J4*J3^3*J2 + 150*J4*J3*J2^4 - 3600*J3^5 + 240*J3^3*J2^3 - 4*J3*J2^6, 16200*J6*J5*J3 + 45360*J6*J4^2 - 17550*J6*J4*J2^2 - 49950*J6*J3^2*J2 + 1665*J6*J2^4 - 14580*J5^2*J4 + 2430*J5^2*J2^2 + 22275*J5*J4*J3*J2 + 43200*J5*J3^3 - 1440*J5*J3*J2^3 + 5022*J4^3*J2 - 34560*J4^2*J3^2 - 2223*J4^2*J2^3 - 7650*J4*J3^2*J2^2 + 255*J4*J2^5 - 3600*J3^4*J2 + 240*J3^2*J2^4 - 4*J2^7, 7620480*J6*J4^3 - 4626720*J6*J4^2*J2^2 - 6609600*J6*J4*J3^2*J2 + 929070*J6*J4*J2^4 + 10368000*J6*J3^4 + 1502550*J6*J3^2*J2^3 - 61605*J6*J2^6 + 874800*J5^3*J3 - 2449440*J5^2*J4^2 + 947700*J5^2*J4*J2^2 - 3207600*J5^2*J3^2*J2 - 89910*J5^2*J2^4 + 3440880*J5*J4^2*J3*J2 + 16912800*J5*J4*J3^3 - 982935*J5*J4*J3*J2^3 - 1555200*J5*J3^3*J2^2 + 51840*J5*J3*J2^5 + 843696*J4^4*J2 - 4581360*J4^3*J3^2 - 559278*J4^3*J2^3 - 168480*J4^2*J3^2*J2^2 + 125091*J4^2*J2^5 - 64800*J4*J3^4*J2 + 305370*J4*J3^2*J2^4 - 10107*J4*J2^7 + 432000*J3^6 + 104400*J3^4*J2^3 - 8400*J3^2*J2^6 + 148*J2^9, 97200*J5^4 - 656100*J5^3*J3*J2 - 437400*J5^2*J4^2*J2 + 2916000*J5^2*J4*J3^2 + 212625*J5^2*J4*J2^3 + 753300*J5^2*J3^2*J2^2 - 25110*J5^2*J2^5 + 2494800*J5*J4^3*J3 - 1336500*J5*J4^2*J3*J2^2 - 5427000*J5*J4*J3^3*J2 + 180900*J5*J4*J3*J2^4 - 3024000*J5*J3^5 + 201600*J5*J3^3*J2^3 - 3360*J5*J3*J2^6 + 381024*J4^5 - 259200*J4^4*J2^2 - 186300*J4^3*J3^2*J2 + 66960*J4^3*J2^4 + 2592000*J4^2*J3^4 + 151200*J4^2*J3^2*J2^3 - 7920*J4^2*J2^6 + 351000*J4*J3^4*J2^2 - 23400*J4*J3^2*J2^5 + 390*J4*J2^8 + 108000*J3^6*J2 - 10800*J3^4*J2^4 + 360*J3^2*J2^7 - 4*J2^10 ]; /* Explicit invariants t <> 0 and D14 <>0 */ JC2p3 := [ t, t, -9800*u^4+85*t*u^2-35/3*t*u+2/147*t^2, -137200*u^5+700*t*u^3+350/3*t*u^2-25/28*t^2*u+1/28*t^2, -617400*u^6+2030*t*u^4+1470*t*u^3-689/56*t^2*u^2+11/12*t^2*u-1/24*t^2+2/3087*t^3, -1920800*u^7-72520/3*t*u^5+43120/3*t*u^4+377/6*t^2*u^3-226/9*t^2*u^2+1/588*t^2*(17*t+686)*u-1/588*t^3, -2469600*u^8-125300/3*t*u^6+37240/3*t*u^5-643/14*t^2*u^4+1432/9*t^2*u^3-1/246960*t^2*(4705960+120087*t)*u^2+1411/17640*t^3*u-11/252105*t^4-1/1680*t^3, 302526000*u^9-12022150/3*t*u^7-325850/3*t*u^6+665105/36*t^2*u^5-9905/18*t^2*u^4-1/2016*t^2*(-397880+56341*t)*u^3+18829/6048*t^3*u^2+1/98784*t^3*(472*t-30527)*u+1/96*t^3-1/4116*t^4, 1162084000*u^10-11872700*t*u^8-7991900/3*t*u^7+1366535/18*t^2*u^6-51835/9*t^2*u^5-1/2352*t^2*(-13267240+268943*t)*u^4-77657/3024*t^3*u^3+1/1037232*t^3*(67571+105696*t)*u^2-1/148176*t^3*(824*t-1029)*u-11/5294205*t^5+1/6174*t^4 ]; /* J2=0, J4=J3 : t <> -105/1260 and D14 <>0 */ JC2p3bis := [ 0, 1260*t+105, 7350*t, 36750*t+7350, -66150*t^2-242550*t-29400, -926100*t^2+977550*t+102900, -7563150*t^2-1749300*t-102900, 20837250*t^3-33957000*t^2-8232000*t-1029000, -6945750*t^3+557975250*t^2+119364000*t+7203000 ]; /* J3=0, J5=J2^2 : D14 <>0 mod p <> 101 */ JC2p3ter := [ 1010/3*(52*t+59)*(t+1), 0, 50/27*(52*t+59)^2*(11272*t^2+23147*t+11767), 25/9*(52*t+59)^3*(17*t+29)^2, -25/486*(52*t+59)^3*(27670948*t^3+88650255*t^2+94796346*t+33852031), 50/81*(52*t+59)^4*(17*t+29)*(38117*t^2+81691*t+43682), -25/3402*(52*t+59)^4*(6266813468*t^4+26795826605*t^3+42971724291*t^2+30632960351*t+8190389165), -125/2916*(52*t+59)^5*(17*t+29)*(11612756*t^3+34093287*t^2+33246138*t+10800599), 125/30618*(52*t+59)^5*(794827443664*t^5+4302413461544*t^4+9310923963145*t^3+10069939679311*t^2+5442845374787*t+1176260576869) ]; /* J3=0, J5=J2^2 : D14 <>0 mod p = 101 */ JC2p3ter_mod101 := [ 1010/3*(52*t+59)*(t+1), 0, 50/27*(52*t+59)^2*(11272*t^2+23147*t+11767), 25/9*(52*t+59)^3*(17*t+29)^2, -25/486*(52*t+59)^3*(27670948*t^3+88650255*t^2+94796346*t+33852031), 50/81*(52*t+59)^4*(17*t+29)*(38117*t^2+81691*t+43682), -25/3402*(52*t+59)^4*(6266813468*t^4+26795826605*t^3+42971724291*t^2+30632960351*t+8190389165), -125/2916*(52*t+59)^5*(17*t+29)*(11612756*t^3+34093287*t^2+33246138*t+10800599), 125/30618*(52*t+59)^5*(794827443664*t^5+4302413461544*t^4+9310923963145*t^3+10069939679311*t^2+5442845374787*t+1176260576869) ]; /* Isolated points mod p <> 13, 17, 101 */ JC2p3qua := [ 1010/39, 0, 563600/4563, 14450/1521, -345886850/533871, 64798900/177957, -78335168350/48582261, -12338553250/20820969, 49676715229000/5684124537 ]; /* Isolated points mod p = 101 */ JC2p3qua_mod101 := [ 32, 0, 57, 14, 11, 93, 91, 4, 52 ]; /*** * C4 stratum --- Eq. (XVIII) in Sec. 3.2.3 of [LR12] ****************************************************/ C4Stratum := [ 4800902400*J10^2 + 262906560*J10*J4^2*J2 - 9485910*J10*J4*J2^3 + 92610*J10*J2^5 - 3541737150*J8^2*J4 + 37507050*J8^2*J2^2 - 555660000*J8*J6^2 - 94382820*J8*J6*J4*J2 + 1049580*J8*J6*J2^3 + 133698600*J8*J4^3 - 793800*J8*J4^2*J2^2 - 23756544*J6^2*J4^2 + 3087000*J6^2*J4*J2^2 + 98280*J6*J4^3*J2 + 47460*J6*J4^2*J2^3 - 980*J6*J4*J2^5 + 3831624*J4^5 + 2010015*J4^4*J2^2 - 102312*J4^3*J2^4 + 1029*J4^2*J2^6, 1543147200*J10*J8 - 793618560*J10*J4^2 + 34292160*J10*J4*J2^2 - 357210*J10*J2^4 - 144670050*J8^2*J2 + 1538248320*J8*J6*J4 - 36435420*J8*J6*J2^2 - 82668600*J8*J4^2*J2 + 1905120*J8*J4*J2^3 + 254016000*J6^3 - 10160640*J6^2*J4*J2 - 38808*J6^2*J2^3 - 50388480*J6*J4^3 + 6373080*J6*J4^2*J2^2 - 278460*J6*J4*J2^4 + 3136*J6*J2^6 - 11809800*J4^4*J2 + 643545*J4^3*J2^3 - 7497*J4^2*J2^5, 2540160*J10*J6 - 317520*J10*J4*J2 + 4410*J10*J2^3 + 1786050*J8^2 + 238140*J8*J6*J2 - 884520*J8*J4^2 + 133056*J6^2*J4 + 47880*J6*J4^2*J2 - 1092*J6*J4*J2^3 - 17496*J4^4 - 2205*J4^3*J2^2 + 49*J4^2*J2^4, J9, 1093705578000*J8^3 + 291654820800*J8^2*J6*J2 - 1104121821600*J8^2*J4^2 + 6076142100*J8^2*J4*J2^2 - 1469076134400*J8*J6^2*J4 + 36726903360*J8*J6^2*J2^2 + 231472080000*J8*J6*J4^2*J2 - 6631246440*J8*J6*J4*J2^3 + 30005640*J8*J6*J2^5 + 267846264000*J8*J4^4 - 23803045560*J8*J4^3*J2^2 + 540101520*J8*J4^2*J2^4 - 3333960*J8*J4*J2^6 - 256048128000*J6^4 + 42247941120*J6^3*J4*J2 - 405409536*J6^3*J2^3 + 8888527872*J6^2*J4^3 - 5893679232*J6^2*J4^2*J2^2 + 274718304*J6^2*J4*J2^4 - 3093174*J6^2*J2^6 - 9523422720*J6*J4^4*J2 + 1237946976*J6*J4^3*J2^3 - 60328800*J6*J4^2*J2^5 + 1037232*J6*J4*J2^7 - 5488*J6*J2^9 + 5509980288*J4^6 - 1031704128*J4^5*J2^2 + 58796766*J4^4*J2^4 - 1091475*J4^3*J2^6 + 6174*J4^2*J2^8, J7, J5, J3 ]; /* Explicit invariants t <> 0 and D14 <>0 */ JC4 := [ t, 0, 1/96*(t+1)*t^2, 0, 3*u^3+(63/80*t-5/16)*u^2+(-1/124416000*(-25+63*t)*(-90720*t+36000)+47/6400*t^2-7/384*t+25/6912-1/64*t^3)*u-1/124416000*(-25+63*t)*(-1269*t^2+3150*t-625+2700*t^3), 0, 8/3*u^4+(2/3*t-10/27)*u^3+(139/3600*t^2+25/1296-1/360*t^3-5/72*t)*u^2+(-17/14400*t^4+241/432000*t^3+25/10368*t-125/279936-139/51840*t^2)*u-125/4478976*t-9707/145152000*t^5+139/2985984*t^2-299/18662400*t^3+82091/967680000*t^4+625/161243136-1/483840*t^6, 0, -5/3*u^5+(-31/48*t+125/432)*u^4+(-23/3360*t^3+155/1728*t-625/31104-3349/40320*t^2)*u^3+(3349/387072*t^2+3125/4478976-775/165888*t-94723/29030400*t^3-1/345600*t^4)*u^2+(-15625/1289945088+86893/580608000*t^5-16745/55738368*t^2+61/3870720*t^6+105073/418037760*t^3+3875/35831808*t-735179/13934592000*t^4)*u+15625/185752092672+736579/401316249600*t^4+83725/24078974976*t^2-23681183/3344302080000*t^5-108523/24078974976*t^3-19375/20639121408*t+734581/139345920000*t^6+1/44236800*t^7 ]; /* J4 = 1/96 : t <> 0 and D14 <>0 */ JC4bis := [ t, 0, t^2/96, 0, (154993*t^3 + 14448*t^2 + 426*t + 4)/(7776000), 0, (80060695*t^4 + 11513824*t^3 + 613284*t^2 + 13888*t + 112)/(44089920000), 0, (-905961157*t^5 - 150709664*t^4 - 9796132*t^3 - 308716*t^2 - 4718*t - 28)/(3174474240000) ]; /* J2=0, J6=J4 : D14 <>0 */ JC4ter := [ 0, 0, 4/3969*(t-9)*(11*t+6), 0, 4/3969*(t+1)*(11*t+6)^2, 0, 32/36756909*(373*t^2+440*t+127)*(11*t+6)^2, 0, -8/992436543*(835*t^2+646*t+51)*(11*t+6)^3 ]; /* Isolated point */ JC4qua := [ 1, 0, 1/96, 0, 154993/7776000, 0, 16012139/8817984000, 0, -905961157/3174474240000 ]; /* Isolated point mod p <> 11 */ JC4cinq := [ 0, 0, 4/43659, 0, 4/43659, 0, 11936/4447585989, 0, -6680/120084821703 ]; /*** * D4 stratum --- Eq. (XXI) in Sec. 3.2.4 of [LR12] **************************************************/ D4Stratum := [ 1/36450*J2^4*J4^2 - 1/1215*J2*J3^2*J4^2 - 1/810*J2^2*J4^3 - 12/1225*J4^4 + 1/90*J3*J4^2*J5 - 26/42525*J2^3*J4*J6 + 52/2835*J3^2*J4*J6 + 76/2835*J2*J4^2*J6 - 2/15*J5^2*J6 + 352/4725*J4*J6^2 + 1/5*J4*J5*J7 - 2/15*J3*J6*J7 - 1/30*J2*J7^2 - 52/105*J4^2*J8 + 2/15*J2*J6*J8 + J8^2 + 1/15*J3*J4*J9 + 1/30*J2*J5*J9 - 2/5*J7*J9 + 1/405*J2^3*J10 - 2/27*J3^2*J10 - 8/45*J2*J4*J10 + 64/45*J6*J10, -1/29160*J2^3*J3*J4^2 + 1/972*J3^3*J4^2 + 1/648*J2*J3*J4^3 - 1/2160*J2^2*J4^2*J5 + 1/1134*J3*J4^2*J6 - 1/2430*J2^3*J5*J6 + 1/81*J3^2*J5*J6 + 31/3780*J2*J4*J5*J6 + 4/135*J5*J6^2 + 1/1620*J2^3*J4*J7 - 1/54*J3^2*J4*J7 - 1/140*J2*J4^2*J7 + 1/180*J2^2*J6*J7 - 17/315*J4*J6*J7 + 1/12*J3*J7^2 - 1/6*J3*J6*J8 - 1/12*J2*J7*J8 - 1/9720*J2^4*J9 + 1/324*J2*J3^2*J9 + 1/540*J2^2*J4*J9 + 2/105*J4^2*J9 - 1/12*J3*J5*J9 - 8/135*J2*J6*J9 + J8*J9 + 1/12*J3*J4*J10 + 1/24*J2*J5*J10 - 1/2*J7*J10, 1/972000*J2^7*J4 - 1/16200*J2^4*J3^2*J4 + 1/1080*J2*J3^4*J4 - 1/10800*J2^5*J4^2 + 1/360*J2^2*J3^2*J4^2 + 311/168000*J2^3*J4^3 + 39/5600*J3^2*J4^3 - 153/2800*J2*J4^4 + 1/1200*J2^3*J3*J4*J5 - 1/40*J3^3*J4*J5 - 3/80*J2*J3*J4^2*J5 + 9/1600*J2^2*J4*J5^2 + 729/5600*J4^2*J5^2 + 13/324000*J2^6*J6 - 13/5400*J2^3*J3^2*J6 + 13/360*J3^4*J6 - 3247/756000*J2^4*J4*J6 + 3247/25200*J2*J3^2*J4*J6 + 941/8400*J2^2*J4^2*J6 - 9/50*J4^3*J6 - 1551/5600*J3*J4*J5*J6 - 351/1600*J2*J5^2*J6 + 1/288*J2^3*J6^2 - 5/48*J3^2*J6^2 + 211/840*J2*J4*J6^2 + J6^3 + 513/800*J3*J4^2*J7 + 3/800*J2^3*J5*J7 - 9/80*J3^2*J5*J7 + 81/1600*J2*J4*J5*J7 - 27/16*J5*J6*J7 + 13/800*J2^3*J4*J8 - 39/80*J3^2*J4*J8 - 549/400*J2*J4^2*J8 + 243/160*J5^2*J8 + 9/2*J4*J6*J8 - 1/400*J2^3*J3*J9 + 3/40*J3^3*J9 + 9/80*J2*J3*J4*J9 - 27/800*J2^2*J5*J9 + 81/100*J4*J5*J9 - 9/4*J3*J6*J9 + 1/400*J2^4*J10 - 3/40*J2*J3^2*J10 - 9/80*J2^2*J4*J10 - 81/25*J4^2*J10 + 81/80*J3*J5*J10 + 9/4*J2*J6*J10, -11/118098000*J2^7*J4 + 11/1968300*J2^4*J3^2*J4 - 11/131220*J2*J3^4*J4 + 19/2624400*J2^5*J4^2 - 19/87480*J2^2*J3^2*J4^2 - 23/637875*J2^3*J4^3 - 43/14175*J3^2*J4^3 - 1/3780*J2*J4^4 - 11/145800*J2^3*J3*J4*J5 + 11/4860*J3^3*J4*J5 + 19/6480*J2*J3*J4^2*J5 - 11/21600*J2^2*J4*J5^2 + 1/1400*J4^2*J5^2 - 7/4374000*J2^6*J6 + 7/72900*J2^3*J3^2*J6 - 7/4860*J3^4*J6 + 15137/91854000*J2^4*J4*J6 - 15137/3061800*J2*J3^2*J4*J6 - 4231/1020600*J2^2*J4^2*J6 - 86/33075*J4^3*J6 - 433/226800*J3*J4*J5*J6 + 103/7200*J2*J5^2*J6 + 1/24300*J2^3*J6^2 - 1/810*J3^2*J6^2 - 511/18225*J2*J4*J6^2 - 103/25200*J3*J4^2*J7 - 11/32400*J2^3*J5*J7 + 11/1080*J3^2*J5*J7 + 3/800*J2*J4*J5*J7 + 1/180*J2*J3*J6*J7 + 1/360*J5*J6*J7 + 1/360*J2^2*J7^2 - 1/40*J4*J7^2 - 23/97200*J2^3*J4*J8 + 23/3240*J3^2*J4*J8 + 191/5400*J2*J4^2*J8 - 11/80*J5^2*J8 - 1/180*J2^2*J6*J8 + 61/189*J4*J6*J8 - 1/12*J3*J7*J8 + 1/8100*J2^3*J3*J9 - 1/270*J3^3*J9 - 1/120*J2*J3*J4*J9 + 1/3600*J2^2*J5*J9 + 2/75*J4*J5*J9 + 2/45*J3*J6*J9 - 1/60*J2*J7*J9 - 11/48600*J2^4*J10 + 11/1620*J2*J3^2*J10 + 7/540*J2^2*J4*J10 - 46/525*J4^2*J10 - 1/20*J3*J5*J10 - 14/135*J2*J6*J10 + J8*J10, 1/10497600*J2^7*J4 - 1/174960*J2^4*J3^2*J4 + 1/11664*J2*J3^4*J4 - 1/139968*J2^5*J4^2 + 5/23328*J2^2*J3^2*J4^2 - 37/907200*J2^3*J4^3 + 461/90720*J3^2*J4^3 - 13/15120*J2*J4^4 + 1/12960*J2^3*J3*J4*J5 - 1/432*J3^3*J4*J5 - 5/1728*J2*J3*J4^2*J5 + 1/1920*J2^2*J4*J5^2 + 31/1120*J4^2*J5^2 + 13/3499200*J2^6*J6 - 13/58320*J2^3*J3^2*J6 + 13/3888*J3^4*J6 - 3107/8164800*J2^4*J4*J6 + 3107/272160*J2*J3^2*J4*J6 + 2603/272160*J2^2*J4^2*J6 + 1/1890*J4^3*J6 - 13/2240*J3*J4*J5*J6 - 157/5760*J2*J5^2*J6 + 31/38880*J2^3*J6^2 - 31/1296*J3^2*J6^2 + 61/3780*J2*J4*J6^2 + 397/20160*J3*J4^2*J7 + 1/2880*J2^3*J5*J7 - 1/96*J3^2*J5*J7 + 29/1920*J2*J4*J5*J7 - 1/144*J2*J3*J6*J7 - 1/96*J5*J6*J7 - 1/288*J2^2*J7^2 - 1/32*J4*J7^2 + 13/8640*J2^3*J4*J8 - 13/288*J3^2*J4*J8 - 163/1440*J2*J4^2*J8 + 9/64*J5^2*J8 + 1/144*J2^2*J6*J8 + 1/12*J4*J6*J8 + 5/48*J3*J7*J8 - 1/9720*J2^3*J3*J9 + 1/324*J3^3*J9 + 7/864*J2*J3*J4*J9 + 1/2880*J2^2*J5*J9 - 3/10*J4*J5*J9 - 5/54*J3*J6*J9 - 1/48*J2*J7*J9 + J9^2 + 1/4320*J2^4*J10 - 1/144*J2*J3^2*J10 - 1/72*J2^2*J4*J10 - 2/15*J4^2*J10 + 1/24*J3*J5*J10 + 1/6*J2*J6*J10, -1/492075*J2^6*J3*J4 + 4/32805*J2^3*J3^3*J4 - 4/2187*J3^5*J4 + 2/10935*J2^4*J3*J4^2 - 4/729*J2*J3^3*J4^2 - 1/243*J2^2*J3*J4^3 + 6/35*J3*J4^4 - 1/18225*J2^5*J4*J5 + 2/1215*J2^2*J3^2*J4*J5 + 509/85050*J2^3*J4^2*J5 - 299/2835*J3^2*J4^2*J5 - 104/675*J2*J4^3*J5 - 1/90*J2*J3*J4*J5^2 + 3/10*J4*J5^3 + 937/382725*J2^3*J3*J4*J6 - 1874/25515*J3^3*J4*J6 - 937/8505*J2*J3*J4^2*J6 + 59/18225*J2^4*J5*J6 - 118/1215*J2*J3^2*J5*J6 - 3193/28350*J2^2*J4*J5*J6 - 1892/4725*J4^2*J5*J6 + 59/45*J3*J5^2*J6 - 9272/8505*J3*J4*J6^2 + 20/81*J2*J5*J6^2 + 1/54675*J2^6*J7 - 4/3645*J2^3*J3^2*J7 + 4/243*J3^4*J7 - 119/36450*J2^4*J4*J7 + 119/1215*J2*J3^2*J4*J7 + 77/2025*J2^2*J4^2*J7 + 16/175*J4^3*J7 - 23/15*J3*J4*J5*J7 - 34/1215*J2^3*J6*J7 + 68/81*J3^2*J6*J7 + 1384/2835*J2*J4*J6*J7 + J5*J7^2 + 97/45*J3*J4^2*J8 + 1/135*J2^3*J5*J8 - 2/9*J3^2*J5*J8 + 49/90*J2*J4*J5*J8 - 6*J5*J6*J8 - 8/3*J4*J7*J8 + 1/6075*J2^5*J9 - 2/405*J2^2*J3^2*J9 - 8/675*J2^3*J4*J9 + 2/15*J3^2*J4*J9 + 148/225*J2*J4^2*J9 + 1/15*J2*J3*J5*J9 - 14/5*J5^2*J9 + 32/135*J2^2*J6*J9 + 32/15*J4*J6*J9 + 4/3*J3*J7*J9 - 2/405*J2^3*J3*J10 + 4/27*J3^3*J10 + 2/9*J2*J3*J4*J10 - 1/15*J2^2*J5*J10 + 64/15*J4*J5*J10 - 64/9*J3*J6*J10 - 4/3*J2*J7*J10, -1/182250*J2^6*J3*J4 + 2/6075*J2^3*J3^3*J4 - 2/405*J3^5*J4 + 1/2025*J2^4*J3*J4^2 - 2/135*J2*J3^3*J4^2 - 1/90*J2^2*J3*J4^3 + 243/700*J3*J4^4 - 1/6750*J2^5*J4*J5 + 1/225*J2^2*J3^2*J4*J5 + 79/5250*J2^3*J4^2*J5 - 44/175*J3^2*J4^2*J5 - 2757/7000*J2*J4^3*J5 - 3/100*J2*J3*J4*J5^2 + 81/100*J4*J5^3 + 517/141750*J2^3*J3*J4*J6 - 517/4725*J3^3*J4*J6 - 517/3150*J2*J3*J4^2*J6 + 13/2250*J2^4*J5*J6 - 13/75*J2*J3^2*J5*J6 - 2213/10500*J2^2*J4*J5*J6 - 1086/875*J4^2*J5*J6 + 117/50*J3*J5^2*J6 - 1369/630*J3*J4*J6^2 + 1/4*J2*J5*J6^2 + 1/20250*J2^6*J7 - 2/675*J2^3*J3^2*J7 + 2/45*J3^4*J7 - 11/1500*J2^4*J4*J7 + 11/50*J2*J3^2*J4*J7 + 29/250*J2^2*J4^2*J7 + 81/250*J4^3*J7 - 117/50*J3*J4*J5*J7 - 2/45*J2^3*J6*J7 + 4/3*J3^2*J6*J7 + 6/5*J2*J4*J6*J7 + J6^2*J7 + 171/50*J3*J4^2*J8 + 1/50*J2^3*J5*J8 - 3/5*J3^2*J5*J8 + 27/100*J2*J4*J5*J8 - 9*J5*J6*J8 + 1/2250*J2^5*J9 - 1/75*J2^2*J3^2*J9 - 29/750*J2^3*J4*J9 + 14/25*J3^2*J4*J9 + 177/125*J2*J4^2*J9 + 9/50*J2*J3*J5*J9 - 243/50*J5^2*J9 + 2/5*J2^2*J6*J9 + 24/5*J4*J6*J9 - 1/75*J2^3*J3*J10 + 2/5*J3^3*J10 + 3/5*J2*J3*J4*J10 - 9/50*J2^2*J5*J10 + 108/25*J4*J5*J10 - 12*J3*J6*J10, -1/7873200*J2^6*J3*J4 + 1/131220*J2^3*J3^3*J4 - 1/8748*J3^5*J4 + 1/77760*J2^4*J3*J4^2 - 1/2592*J2*J3^3*J4^2 - 5/15552*J2^2*J3*J4^3 + 1/280*J3*J4^4 - 1/291600*J2^5*J4*J5 + 1/9720*J2^2*J3^2*J4*J5 + 527/1814400*J2^3*J4^2*J5 - 53/15120*J3^2*J4^2*J5 - 1/200*J2*J4^3*J5 - 1/1440*J2*J3*J4*J5^2 + 3/160*J4*J5^3 + 307/6123600*J2^3*J3*J4*J6 - 307/204120*J3^3*J4*J6 - 13/5670*J2*J3*J4^2*J6 + 1/12150*J2^4*J5*J6 - 1/405*J2*J3^2*J5*J6 - 589/226800*J2^2*J4*J5*J6 - 33/1400*J4^2*J5*J6 + 19/720*J3*J5^2*J6 - 11/486*J3*J4*J6^2 - 17/2160*J2*J5*J6^2 + 1/874800*J2^6*J7 - 1/14580*J2^3*J3^2*J7 + 1/972*J3^4*J7 - 7/48600*J2^4*J4*J7 + 7/1620*J2*J3^2*J4*J7 + 241/151200*J2^2*J4^2*J7 + 3/1400*J4^3*J7 - 1/80*J3*J4*J5*J7 - 23/38880*J2^3*J6*J7 + 7/648*J3^2*J6*J7 + 97/5040*J2*J4*J6*J7 - 1/288*J2*J3*J7^2 + 37/720*J3*J4^2*J8 + 1/2160*J2^3*J5*J8 - 1/72*J3^2*J5*J8 - 7/480*J2*J4*J5*J8 + 1/144*J2*J3*J6*J8 + 1/48*J5*J6*J8 + 1/288*J2^2*J7*J8 - 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