Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828a |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
198720 |
Modular degree for the optimal curve |
Δ |
41348200228368 = 24 · 3 · 11 · 238 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 11+ -4 -5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-20278,1074301] |
[a1,a2,a3,a4,a6] |
Generators |
[-25:1251:1] |
Generators of the group modulo torsion |
j |
736000/33 |
j-invariant |
L |
3.2183709669637 |
L(r)(E,1)/r! |
Ω |
0.63710867235652 |
Real period |
R |
5.0515259112476 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000852 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69828j1 |
Quadratic twists by: -23 |