Atkin-Lehner |
2+ 3- 5- 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030q |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
357120 |
Modular degree for the optimal curve |
Δ |
530749019531250 = 2 · 311 · 59 · 13 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 5- 1 5 13+ 6 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-32724,1998918] |
[a1,a2,a3,a4,a6] |
Generators |
[57:534:1] |
Generators of the group modulo torsion |
j |
5316218237037889/728050781250 |
j-invariant |
L |
5.8244747378143 |
L(r)(E,1)/r! |
Ω |
0.50073536693415 |
Real period |
R |
0.64621345177741 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995373 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23010q1 |
Quadratic twists by: -3 |