Atkin-Lehner |
2- 3- 5+ 11+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
58410w |
Isogeny class |
Conductor |
58410 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
337920 |
Modular degree for the optimal curve |
Δ |
7406310508621200 = 24 · 311 · 52 · 116 · 59 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 11+ -4 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-51233,-1653919] |
[a1,a2,a3,a4,a6] |
Generators |
[-195:1042:1] |
Generators of the group modulo torsion |
j |
20400349049336521/10159548022800 |
j-invariant |
L |
8.5439414030377 |
L(r)(E,1)/r! |
Ω |
0.33410438314065 |
Real period |
R |
3.1965838499788 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000236 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19470r1 |
Quadratic twists by: -3 |