Atkin-Lehner |
2- 3- 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
89712bi |
Isogeny class |
Conductor |
89712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
57600 |
Modular degree for the optimal curve |
Δ |
-813867264 = -1 · 28 · 36 · 72 · 89 |
Discriminant |
Eigenvalues |
2- 3- 3 7- -6 -4 7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-831,9322] |
[a1,a2,a3,a4,a6] |
Generators |
[18:14:1] |
Generators of the group modulo torsion |
j |
-340062928/4361 |
j-invariant |
L |
8.1380565130472 |
L(r)(E,1)/r! |
Ω |
1.5942353823743 |
Real period |
R |
2.5523384438793 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003679 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22428e1 9968k1 |
Quadratic twists by: -4 -3 |