Atkin-Lehner |
2+ 3- 5- 23- 41- |
Signs for the Atkin-Lehner involutions |
Class |
84870s |
Isogeny class |
Conductor |
84870 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
598022175622500 = 22 · 38 · 54 · 232 · 413 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 -6 0 -8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-119754,-15877472] |
[a1,a2,a3,a4,a6] |
Generators |
[-198:304:1] |
Generators of the group modulo torsion |
j |
260536340891076769/820332202500 |
j-invariant |
L |
3.6020557143602 |
L(r)(E,1)/r! |
Ω |
0.25669008127638 |
Real period |
R |
0.58469596473971 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003598 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28290i1 |
Quadratic twists by: -3 |