Atkin-Lehner |
2+ 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bn |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
401783570496 = 26 · 32 · 78 · 112 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11+ 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2662,-44080] |
[a1,a2,a3,a4,a6] |
Generators |
[51987:2280950:27] |
Generators of the group modulo torsion |
j |
277167808/53361 |
j-invariant |
L |
9.2358407197101 |
L(r)(E,1)/r! |
Ω |
0.67352878040492 |
Real period |
R |
6.8563073980313 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999952 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
51744u1 103488gm2 7392b1 |
Quadratic twists by: -4 8 -7 |