Atkin-Lehner |
2+ 3- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744bk |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-5431878144 = -1 · 29 · 39 · 72 · 11 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- 11+ 2 3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-296,-4152] |
[a1,a2,a3,a4,a6] |
Generators |
[34:-162:1] |
Generators of the group modulo torsion |
j |
-114709448/216513 |
j-invariant |
L |
6.7980112892774 |
L(r)(E,1)/r! |
Ω |
0.5417689958116 |
Real period |
R |
0.69710023417751 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999565 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744cc1 103488bt1 51744c1 |
Quadratic twists by: -4 8 -7 |