Atkin-Lehner |
2+ 3- 13+ 73+ |
Signs for the Atkin-Lehner involutions |
Class |
68328b |
Isogeny class |
Conductor |
68328 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
-55985201723333376 = -1 · 28 · 39 · 134 · 733 |
Discriminant |
Eigenvalues |
2+ 3- 1 2 -4 13+ 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-133572,-21969308] |
[a1,a2,a3,a4,a6] |
j |
-1412220478557184/299989292499 |
j-invariant |
L |
1.9753674555618 |
L(r)(E,1)/r! |
Ω |
0.12346046655927 |
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 |
22776f1 |
Quadratic twists by: -3 |