Atkin-Lehner |
2- 3- 5- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
81840dh |
Isogeny class |
Conductor |
81840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
1946938245120 = 220 · 32 · 5 · 113 · 31 |
Discriminant |
Eigenvalues |
2- 3- 5- 0 11+ -2 2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-619000,187243220] |
[a1,a2,a3,a4,a6] |
Generators |
[31172:79281:64] |
Generators of the group modulo torsion |
j |
6403780138352571001/475326720 |
j-invariant |
L |
8.6509358333402 |
L(r)(E,1)/r! |
Ω |
0.63182713116393 |
Real period |
R |
6.845967362559 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999952434 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10230j1 |
Quadratic twists by: -4 |