Atkin-Lehner |
2+ 3+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
9306b |
Isogeny class |
Conductor |
9306 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
8024160177487872 = 224 · 39 · 11 · 472 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -2 11- -2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-50532,-723376] |
[a1,a2,a3,a4,a6] |
j |
724997846257875/407669571584 |
j-invariant |
L |
0.68524003126657 |
L(r)(E,1)/r! |
Ω |
0.34262001563328 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
74448o1 9306h1 102366z1 |
Quadratic twists by: -4 -3 -11 |