Atkin-Lehner |
2- 3+ 7+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
31164b |
Isogeny class |
Conductor |
31164 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
133056 |
Modular degree for the optimal curve |
Δ |
1112287176906192 = 24 · 34 · 78 · 533 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -1 3 -7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-29269,1077490] |
[a1,a2,a3,a4,a6] |
j |
30064771072/12059037 |
j-invariant |
L |
0.88890425593052 |
L(r)(E,1)/r! |
Ω |
0.44445212796362 |
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 |
124656db1 93492h1 31164m1 |
Quadratic twists by: -4 -3 -7 |