Atkin-Lehner |
2+ 3+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
68544d |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
506880 |
Modular degree for the optimal curve |
Δ |
97899233596416 = 210 · 39 · 75 · 172 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 2 6 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-605664,-181423800] |
[a1,a2,a3,a4,a6] |
Generators |
[-10007081689246950:142380533227580:22304316191949] |
Generators of the group modulo torsion |
j |
1219067475001344/4857223 |
j-invariant |
L |
8.0620736333872 |
L(r)(E,1)/r! |
Ω |
0.17113613456233 |
Real period |
R |
23.554562730002 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994422 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544dc1 4284a1 68544k1 |
Quadratic twists by: -4 8 -3 |