Atkin-Lehner |
2- 3- 7+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
23688r |
Isogeny class |
Conductor |
23688 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-3868155648 = -1 · 28 · 38 · 72 · 47 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 2 -4 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-111,3026] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:54:1] [-10:56:1] |
Generators of the group modulo torsion |
j |
-810448/20727 |
j-invariant |
L |
6.9918332845751 |
L(r)(E,1)/r! |
Ω |
1.168410711146 |
Real period |
R |
0.74800680294572 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47376p1 7896a1 |
Quadratic twists by: -4 -3 |