Atkin-Lehner |
13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
36517a |
Isogeny class |
Conductor |
36517 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
112320 |
Modular degree for the optimal curve |
Δ |
15271244817881 = 13 · 537 |
Discriminant |
Eigenvalues |
1 2 2 2 2 13+ -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-39384,2986115] |
[a1,a2,a3,a4,a6] |
Generators |
[340582577984184125085550:-3636197723904586499429609:4741674336126000125000] |
Generators of the group modulo torsion |
j |
304821217/689 |
j-invariant |
L |
11.900945486423 |
L(r)(E,1)/r! |
Ω |
0.70118753791345 |
Real period |
R |
33.945114089838 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
689a1 |
Quadratic twists by: 53 |