Atkin-Lehner |
5+ 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
31265c |
Isogeny class |
Conductor |
31265 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1053696 |
Modular degree for the optimal curve |
Δ |
398497203001015625 = 57 · 1310 · 37 |
Discriminant |
Eigenvalues |
1 2 5+ 2 0 13+ 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-10167888,12475142867] |
[a1,a2,a3,a4,a6] |
Generators |
[709188380598782386785416640:-658511408150517088936361459:383021606560731070464000] |
Generators of the group modulo torsion |
j |
24085514417143530961/82559140625 |
j-invariant |
L |
9.5556937496033 |
L(r)(E,1)/r! |
Ω |
0.26227337327307 |
Real period |
R |
36.434097866481 |
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 |
2405c1 |
Quadratic twists by: 13 |