Atkin-Lehner |
2- 11+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
8272h |
Isogeny class |
Conductor |
8272 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
34560 |
Modular degree for the optimal curve |
Δ |
-8127578141360128 = -1 · 230 · 115 · 47 |
Discriminant |
Eigenvalues |
2- 0 0 5 11+ 1 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-14315,-4387302] |
[a1,a2,a3,a4,a6] |
Generators |
[13763386:378841633:17576] |
Generators of the group modulo torsion |
j |
-79202305058625/1984272007168 |
j-invariant |
L |
4.7836923694468 |
L(r)(E,1)/r! |
Ω |
0.17967102973833 |
Real period |
R |
13.312364203661 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1034b1 33088bf1 74448bk1 90992u1 |
Quadratic twists by: -4 8 -3 -11 |