Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828d |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
-147476736 = -1 · 28 · 32 · 112 · 232 |
Discriminant |
Eigenvalues |
2- 3+ 1 0 11+ 7 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,100,408] |
[a1,a2,a3,a4,a6] |
Generators |
[14:66:1] |
Generators of the group modulo torsion |
j |
808496/1089 |
j-invariant |
L |
5.8632239273351 |
L(r)(E,1)/r! |
Ω |
1.2351351576265 |
Real period |
R |
0.39558585220727 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000486 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69828n1 |
Quadratic twists by: -23 |