Atkin-Lehner |
5+ 29+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
7685a |
Isogeny class |
Conductor |
7685 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8832 |
Modular degree for the optimal curve |
Δ |
526489367185 = 5 · 294 · 533 |
Discriminant |
Eigenvalues |
-1 0 5+ -2 0 2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-15228,-718618] |
[a1,a2,a3,a4,a6] |
Generators |
[9340:897866:1] |
Generators of the group modulo torsion |
j |
390504083161555089/526489367185 |
j-invariant |
L |
1.9663004717923 |
L(r)(E,1)/r! |
Ω |
0.42980971486982 |
Real period |
R |
9.1496325176727 |
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 |
122960g1 69165r1 38425d1 |
Quadratic twists by: -4 -3 5 |