Atkin-Lehner |
2- 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264z |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
4252041216 = 216 · 36 · 89 |
Discriminant |
Eigenvalues |
2- 3- 2 4 0 -4 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1164,-14960] |
[a1,a2,a3,a4,a6] |
Generators |
[860:25200:1] |
Generators of the group modulo torsion |
j |
3650692/89 |
j-invariant |
L |
8.165638993866 |
L(r)(E,1)/r! |
Ω |
0.81857147205519 |
Real period |
R |
4.987737340344 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000056 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51264k1 12816b1 5696p1 |
Quadratic twists by: -4 8 -3 |