Atkin-Lehner |
2- 3- 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
69264r |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
478526482512 = 24 · 314 · 132 · 37 |
Discriminant |
Eigenvalues |
2- 3- -2 0 0 13+ 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-18516,969199] |
[a1,a2,a3,a4,a6] |
Generators |
[89:162:1] |
Generators of the group modulo torsion |
j |
60189081714688/41025933 |
j-invariant |
L |
4.970757541592 |
L(r)(E,1)/r! |
Ω |
0.92488279097886 |
Real period |
R |
2.687236474522 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000885 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17316a1 23088n1 |
Quadratic twists by: -4 -3 |