Atkin-Lehner |
2+ 3+ 7+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
67536b |
Isogeny class |
Conductor |
67536 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-147701232 = -1 · 24 · 39 · 7 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ -1 1 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,81,513] |
[a1,a2,a3,a4,a6] |
Generators |
[96:945:1] |
Generators of the group modulo torsion |
j |
186624/469 |
j-invariant |
L |
7.6164138780966 |
L(r)(E,1)/r! |
Ω |
1.2799940322498 |
Real period |
R |
2.9751755422259 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000272 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33768m1 67536e1 |
Quadratic twists by: -4 -3 |