Atkin-Lehner |
2- 3- 5+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
57330ef |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
10069958076272640 = 212 · 38 · 5 · 78 · 13 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 0 13- 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-272768,54687651] |
[a1,a2,a3,a4,a6] |
Generators |
[93:5441:1] |
Generators of the group modulo torsion |
j |
26168974809769/117411840 |
j-invariant |
L |
9.8529007988966 |
L(r)(E,1)/r! |
Ω |
0.40943388812695 |
Real period |
R |
1.0026955393567 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000024 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19110o1 8190br1 |
Quadratic twists by: -3 -7 |