Atkin-Lehner |
2- 29+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
8468b |
Isogeny class |
Conductor |
8468 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
3312 |
Modular degree for the optimal curve |
Δ |
2888062208 = 28 · 29 · 733 |
Discriminant |
Eigenvalues |
2- -2 0 2 -3 -4 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-413,-2081] |
[a1,a2,a3,a4,a6] |
Generators |
[25:62:1] |
Generators of the group modulo torsion |
j |
30505984000/11281493 |
j-invariant |
L |
2.9024564917941 |
L(r)(E,1)/r! |
Ω |
1.0918148319108 |
Real period |
R |
2.6583779657164 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
33872e1 76212l1 |
Quadratic twists by: -4 -3 |