Atkin-Lehner |
7- 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
47971j |
Isogeny class |
Conductor |
47971 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
19968 |
Modular degree for the optimal curve |
Δ |
-8868734567 = -1 · 77 · 112 · 89 |
Discriminant |
Eigenvalues |
-1 0 2 7- 11- 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,456,2426] |
[a1,a2,a3,a4,a6] |
Generators |
[510:4031:8] |
Generators of the group modulo torsion |
j |
89314623/75383 |
j-invariant |
L |
3.8172972729905 |
L(r)(E,1)/r! |
Ω |
0.84379225696288 |
Real period |
R |
4.523977604067 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000014 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6853g1 |
Quadratic twists by: -7 |