Atkin-Lehner |
2- 5+ 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440cn |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-2430400000000 = -1 · 212 · 58 · 72 · 31 |
Discriminant |
Eigenvalues |
2- 2 5+ 7+ 2 4 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,359,74841] |
[a1,a2,a3,a4,a6] |
Generators |
[-21:240:1] |
Generators of the group modulo torsion |
j |
1245766976/593359375 |
j-invariant |
L |
8.945088558553 |
L(r)(E,1)/r! |
Ω |
0.63436940386854 |
Real period |
R |
3.5251891499543 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000259 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440cw1 34720ba1 |
Quadratic twists by: -4 8 |