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_4_12.txt
N := 3;
X := (u^10 - 4*u^9 + 5*u^8 - 4*u^6 + 5*u^4 - 4*u^3 + u^2)*v^8 + (8*u^10 - 16*u^9 - 8*u^8 + 32*u^7 - 32*u^5 + 8*u^4 + 16*u^3 - 8*u^2)*v^7 + (20*u^10 + 16*u^9 - 92*u^8 + 112*u^6 - 92*u^4 + 16*u^3 + 20*u^2)*v^6 + (8*u^10 + 112*u^9 - 8*u^8 - 224*u^7 + 224*u^5 + 8*u^4 - 112*u^3 - 8*u^2)*v^5 - (28*u^10 - 40*u^9 - 254*u^8 + 276*u^6 - 254*u^4 - 40*u^3 + 28*u^2)*v^4 - (16*u^10 + 128*u^9 + 8*u^8 - 208*u^7 + 208*u^5 - 8*u^4 - 128*u^3 - 16*u^2)*v^3 + (16*u^10 - 16*u^9 - 156*u^8 - 96*u^7 - 8*u^6 - 96*u^5 - 156*u^4 - 16*u^3 + 16*u^2)*v^2 + (32*u^9 + 24*u^8 - 16*u^7 + 16*u^5 - 24*u^4 - 32*u^3)*v + u^12 + 4*u^11 + 9*u^10 + 16*u^9 + 36*u^8 + 40*u^7 + 44*u^6 + 40*u^5 + 36*u^4 + 16*u^3 + 9*u^2 + 4*u + 1;
Xi := u^6 + i*u^5*v^4 + 4*i*u^5*v^3 + 2*i*u^5*v^2 - 4*i*u^5*v + (i + 2)*u^5 + (-2*i - 1)*u^4*v^4 - 4*u^4*v^3 + (12*i - 2)*u^4*v^2 + 4*u^4*v + (-2*i + 2)*u^4 + 2*u^3*v^4 - 8*i*u^3*v^3 - 12*u^3*v^2 + 8*i*u^3*v + 6*u^3 + (2*i - 1)*u^2*v^4 + 4*u^2*v^3 + (-12*i - 2)*u^2*v^2 - 4*u^2*v + (2*i + 2)*u^2 - i*u*v^4 + 4*i*u*v^3 - 2*i*u*v^2 - 4*i*u*v + (-i + 2)*u + 1;
q := (u*v + u - v + 1)/2;
t := (u*v + u - v + 1)/(2*u);
E := [1,(q^2-1)*(t^2-1)/16,(q^2-1)*(t^2-1)/16,0,0];
P := [(q+1)*(t^2-1)/8,(q+1)^2*(t-1)^2*(t+1)/32];
Q := [0,0];
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