Atkin-Lehner |
2+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
31328f |
Isogeny class |
Conductor |
31328 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
689216 = 26 · 112 · 89 |
Discriminant |
Eigenvalues |
2+ -2 2 2 11- -6 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-22,0] |
[a1,a2,a3,a4,a6] |
Generators |
[8:20:1] |
Generators of the group modulo torsion |
j |
19248832/10769 |
j-invariant |
L |
4.8901336647805 |
L(r)(E,1)/r! |
Ω |
2.4767051893601 |
Real period |
R |
1.974451253136 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31328b1 62656p1 |
Quadratic twists by: -4 8 |