Atkin-Lehner |
2+ 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bm |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
-60379349184 = -1 · 26 · 36 · 76 · 11 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11+ 2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,278,11780] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:90:1] |
Generators of the group modulo torsion |
j |
314432/8019 |
j-invariant |
L |
8.8158818445485 |
L(r)(E,1)/r! |
Ω |
0.83306689956277 |
Real period |
R |
1.7637402728684 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000038 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51744t1 103488gl2 1056b1 |
Quadratic twists by: -4 8 -7 |