Atkin-Lehner |
2- 3- 5- 7- |
Signs for the Atkin-Lehner involutions |
Class |
117600hs |
Isogeny class |
Conductor |
117600 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
5308416 |
Modular degree for the optimal curve |
Δ |
129678374952000 = 26 · 39 · 53 · 77 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 2 -2 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-45008378,116206948248] |
[a1,a2,a3,a4,a6] |
Generators |
[3868:540:1] |
Generators of the group modulo torsion |
j |
10713357105862263488/137781 |
j-invariant |
L |
9.31497040521 |
L(r)(E,1)/r! |
Ω |
0.29671349478995 |
Real period |
R |
0.87205058963841 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999937101 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117600br1 117600bn1 16800bk1 |
Quadratic twists by: -4 5 -7 |