Atkin-Lehner |
2+ 3+ 11+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
37488c |
Isogeny class |
Conductor |
37488 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
384000 |
Modular degree for the optimal curve |
Δ |
172851951469824 = 28 · 310 · 115 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ -3 5 11+ -1 -7 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-249657,-47926251] |
[a1,a2,a3,a4,a6] |
Generators |
[-43178676:4902039:148877] |
Generators of the group modulo torsion |
j |
6722282026842016768/675202935429 |
j-invariant |
L |
3.9795812889193 |
L(r)(E,1)/r! |
Ω |
0.21358270883665 |
Real period |
R |
9.3162534331514 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999922 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
18744e1 112464o1 |
Quadratic twists by: -4 -3 |