Atkin-Lehner |
2+ 3+ 23+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
51888c |
Isogeny class |
Conductor |
51888 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
17408 |
Modular degree for the optimal curve |
Δ |
89662464 = 210 · 34 · 23 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 0 0 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-384,-2736] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:6:1] [-10:2:1] |
Generators of the group modulo torsion |
j |
6131234308/87561 |
j-invariant |
L |
6.4264244658947 |
L(r)(E,1)/r! |
Ω |
1.0791904293966 |
Real period |
R |
2.9774283994949 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999967 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
25944d1 |
Quadratic twists by: -4 |