J = smoothplanepicinit(x^4+2*y^4+x^3-3*x*y-2,29,3) W = picrand(J) picmember(J,W) piciszero(J,W) W2 = picrand(J); piceq(J,W,W2) picadd(J,W,W2) factor(piccard(J)) W = picrandtors(J,13); picmember(J,W) piciszero(J,picmul(J,W,13)) piciszero(J,W) picistorsion(J,W,13) P = pictorspairinginit(J,13); X = picrand(J); pictorspairing(J,P,W,X) pictorspairing(J,P,picmul(J,W,2),X) FW = picfrob(J,W); pictorspairing(J,P,FW,X) piceq(J,picmul(J,W,9),picfrob(J,W)) J2 = picsetprec(J,21); \\ Now mod 29^e, e=21 Y = picrand(J2) picmul(J2,Y,-3) picmember(J2,W) picmemberval(J2,W) picmemberval(J2,Y) W2 = piclifttors(J2,W,13); picmember(J2,W2) picistorsion(J2,W2,13) piciszero(J2,W2) piceq(J2,picmul(J2,W2,9),picfrob(J2,W2)) f = x^3*y+y^3+x; P = [1,0,0]; \\ Points on C Q = [0,1,0]; \\ Needed to construct J -> A1 l = 2; \\ Look at J[2] p = 5; e = 60; \\ Work mod 5^60 R = smoothplanegalrep(f,l,p,e,[[P],[Q]]) fa = factor(R[1]) Mat(apply(polredabs,fa[,1])) h = x^3+x+1; \\ C : y^2+h(x)*y = f(x) f = x^5+x^4; \\ Good reduction away from 13 P = [-1,0]; \\ Points on C Q= [0,0]; \\ Needed to construct J -> A1 p = 17; e = 30; \\ Work mod 17^30 l = 7; \\ Look at piece of J[7] chi = x^2-x-2; \\ Where Frob17 acts like this R = hyperellgalrep([f,h],l,p,e,[P,Q],chi) PR = projgalrep(R); F = polredabs(PR[1]) polgalois(F) factor(nfdisc(F)) S = mfinit([16,2,0],1); f = mfeigenbasis(S[1])[1]; R = mfgalrep(f,[5,[[2,2]]],[30,50],5) factor(projgalrep(R)[1]) f = mfDelta(); R = mfgalrep(f,17,100,200) F = polredbest(projgalrep(R)[1]) factor(nfdisc(F))