Atkin-Lehner |
2- 5+ 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440cu |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
-1648115000000 = -1 · 26 · 57 · 73 · 312 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- -1 -3 5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-133161,-18658889] |
[a1,a2,a3,a4,a6] |
Generators |
[13710:179893:27] |
Generators of the group modulo torsion |
j |
-4080168919667961856/25751796875 |
j-invariant |
L |
4.3183590908249 |
L(r)(E,1)/r! |
Ω |
0.12496110611626 |
Real period |
R |
5.7596042280017 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000201 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69440i1 17360bi1 |
Quadratic twists by: -4 8 |