Atkin-Lehner |
2- 3+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828o |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
851904 |
Modular degree for the optimal curve |
Δ |
769610018292551568 = 24 · 317 · 113 · 234 |
Discriminant |
Eigenvalues |
2- 3+ 2 0 11- 4 -7 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-229762,-3851747] |
[a1,a2,a3,a4,a6] |
j |
299591084078848/171885556953 |
j-invariant |
L |
2.1305915459792 |
L(r)(E,1)/r! |
Ω |
0.23673239457371 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69828f1 |
Quadratic twists by: -23 |