Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825r |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
229376 |
Modular degree for the optimal curve |
Δ |
-35939931234375 = -1 · 3 · 56 · 79 · 19 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- -6 -6 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,7325,-155000] |
[a1,a2,a3,a4,a6] |
Generators |
[24:176:1] |
Generators of the group modulo torsion |
j |
68921/57 |
j-invariant |
L |
3.2854768637362 |
L(r)(E,1)/r! |
Ω |
0.36053882372647 |
Real period |
R |
4.5563426822002 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004462 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2793k1 69825bs1 |
Quadratic twists by: 5 -7 |