Atkin-Lehner |
2+ 3- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744bd |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
23808 |
Modular degree for the optimal curve |
Δ |
-3569922048 = -1 · 212 · 3 · 74 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 11- -1 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,131,-2773] |
[a1,a2,a3,a4,a6] |
Generators |
[13:36:1] |
Generators of the group modulo torsion |
j |
25088/363 |
j-invariant |
L |
5.9159527682175 |
L(r)(E,1)/r! |
Ω |
0.68723830968841 |
Real period |
R |
2.1520747187585 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000079 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bs1 103488d1 51744s1 |
Quadratic twists by: -4 8 -7 |