Atkin-Lehner |
2+ 3- 7- 13- 61- |
Signs for the Atkin-Lehner involutions |
Class |
33306j |
Isogeny class |
Conductor |
33306 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5120 |
Modular degree for the optimal curve |
Δ |
1398852 = 22 · 32 · 72 · 13 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- -4 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-31,-34] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:5:1] |
Generators of the group modulo torsion |
j |
3144219625/1398852 |
j-invariant |
L |
4.8949159608455 |
L(r)(E,1)/r! |
Ω |
2.1168307987051 |
Real period |
R |
1.1561897067634 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99918bg1 |
Quadratic twists by: -3 |