Atkin-Lehner |
3+ 5- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825bd |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
82080 |
Modular degree for the optimal curve |
Δ |
-186563671875 = -1 · 33 · 58 · 72 · 192 |
Discriminant |
Eigenvalues |
0 3+ 5- 7- 0 -2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-12833,-555682] |
[a1,a2,a3,a4,a6] |
Generators |
[87234:1215724:343] |
Generators of the group modulo torsion |
j |
-12211978240/9747 |
j-invariant |
L |
3.6717168853607 |
L(r)(E,1)/r! |
Ω |
0.22426624053832 |
Real period |
R |
8.1860668743055 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999916 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69825bk1 69825cd1 |
Quadratic twists by: 5 -7 |