Atkin-Lehner |
2+ 5+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
69290d |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
220800 |
Modular degree for the optimal curve |
Δ |
-391593959380000 = -1 · 25 · 54 · 132 · 415 |
Discriminant |
Eigenvalues |
2+ 0 5+ 3 -2 13+ -4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,16030,-548300] |
[a1,a2,a3,a4,a6] |
Generators |
[45:490:1] [25155:398156:125] |
Generators of the group modulo torsion |
j |
2695394481678639/2317124020000 |
j-invariant |
L |
7.633135673944 |
L(r)(E,1)/r! |
Ω |
0.29433959317393 |
Real period |
R |
2.5933091745077 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999422 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69290u1 |
Quadratic twists by: 13 |