Atkin-Lehner |
2- 3- 5+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300ba |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
-91693255500000000 = -1 · 28 · 39 · 59 · 7 · 113 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 11+ -2 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,58200,-13529500] |
[a1,a2,a3,a4,a6] |
Generators |
[340:-6750:1] |
Generators of the group modulo torsion |
j |
7476617216/31444875 |
j-invariant |
L |
4.947659352968 |
L(r)(E,1)/r! |
Ω |
0.17147611280084 |
Real period |
R |
0.60111134330572 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000933 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23100d1 13860v1 |
Quadratic twists by: -3 5 |