Atkin-Lehner |
2- 3+ 5+ 13+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
69030y |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
46 |
Product of Tamagawa factors cp |
deg |
1642752 |
Modular degree for the optimal curve |
Δ |
3669828304896000 = 223 · 33 · 53 · 133 · 59 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -1 -1 13+ 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-9671438,-11574278883] |
[a1,a2,a3,a4,a6] |
Generators |
[-1795:903:1] |
Generators of the group modulo torsion |
j |
3705382636318975619061027/135919566848000 |
j-invariant |
L |
8.489250030205 |
L(r)(E,1)/r! |
Ω |
0.08561045320512 |
Real period |
R |
2.1556820083393 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69030c1 |
Quadratic twists by: -3 |