Atkin-Lehner |
2- 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776l |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
-134497511407616 = -1 · 218 · 78 · 89 |
Discriminant |
Eigenvalues |
2- -1 1 7- 0 -4 7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-32160,2299648] |
[a1,a2,a3,a4,a6] |
Generators |
[138:686:1] |
Generators of the group modulo torsion |
j |
-7633736209/279104 |
j-invariant |
L |
5.6971178590644 |
L(r)(E,1)/r! |
Ω |
0.57994830851847 |
Real period |
R |
1.2279365624432 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000367 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8722n1 9968m1 |
Quadratic twists by: -4 -7 |