Atkin-Lehner |
2+ 3+ 23- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
51888d |
Isogeny class |
Conductor |
51888 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
268800 |
Modular degree for the optimal curve |
Δ |
700194826158336 = 28 · 314 · 233 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 4 2 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-193532,32809920] |
[a1,a2,a3,a4,a6] |
j |
3131441804230978768/2735136039681 |
j-invariant |
L |
1.5161944930743 |
L(r)(E,1)/r! |
Ω |
0.50539816448573 |
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 |
25944c1 |
Quadratic twists by: -4 |