https://github.com/koffie/mdmagma
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Tip revision: f69d0e06f67b9ac6f57e7d8e6ba3b3d69e650352 authored by Maarten Derickx on 02 November 2020, 22:43:35 UTC
Quickly lists all non cuspidal places up to diamond operators on X_1(N)
Tip revision: f69d0e0
X1_6_12.txt
m:=6; n:= 2; // z = zeta_m
Xz := u^8*v^6 + (u^11 + 3*u^10 + 2*u^8 + 2*u^7 + 3*u^5 + u^4)*v^5 - (u^12 + 4*u^11 - 3*u^10 - 8*u^9 - 12*u^8 - 24*u^7 - 12*u^6 - 8*u^5 - 3*u^4 + 4*u^3 + u^2)*v^4 + (u^13 + 5*u^12 + 7*u^11 + 9*u^10 + 21*u^9 + 13*u^8 + 24*u^7 + 24*u^6 + 13*u^5 + 21*u^4 + 9*u^3 + 7*u^2 + 5*u + 1)*v^3 + (2*u^12 + 8*u^11 + 11*u^10 + 22*u^9 + 30*u^8 + 26*u^7 + 42*u^6 + 26*u^5 + 30*u^4 + 22*u^3 + 11*u^2 + 8*u + 2)*v^2 + (2*u^11 + 6*u^10 + 10*u^9 + 22*u^8 + 24*u^7 + 32*u^6 + 32*u^5 + 24*u^4 + 22*u^3 + 10*u^2 + 6*u + 2)*v + u^10 + 2*u^9 + 5*u^8 + 8*u^7 + 10*u^6 + 12*u^5 + 10*u^4 + 8*u^3 + 5*u^2 + 2*u + 1;
r := (u^2 + 1)/(u^2 - u);
s := (u^2 + u + 1)/u^2;
q := (u+1)*(u^2+v+1)/(u^2*(u-1)^2);
E:=[s-r*s+1,r*s-r^2*s,r*s-r^2*s,0,0];
P:=[0,0]; // point of order mn
Qx:=[q]; // Q=[q,t] is a point of order n, where t is defined over Q(zeta_m)
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