Atkin-Lehner |
2- 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744cj |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
3616052134464 = 26 · 34 · 78 · 112 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 11+ -2 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4034,35496] |
[a1,a2,a3,a4,a6] |
j |
964430272/480249 |
j-invariant |
L |
2.7962750403377 |
L(r)(E,1)/r! |
Ω |
0.6990687601627 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
51744x1 103488bw2 7392i1 |
Quadratic twists by: -4 8 -7 |