Atkin-Lehner |
2+ 3- 5+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
57330u |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
3440640 |
Modular degree for the optimal curve |
Δ |
11829519531648000 = 210 · 313 · 53 · 73 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- 2 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-60637320,181758335296] |
[a1,a2,a3,a4,a6] |
Generators |
[2096:251672:1] |
Generators of the group modulo torsion |
j |
98610250747761380828647/47309184000 |
j-invariant |
L |
4.0400350980669 |
L(r)(E,1)/r! |
Ω |
0.24424461961338 |
Real period |
R |
2.0676172439185 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000226 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19110bz1 57330cr1 |
Quadratic twists by: -3 -7 |