Atkin-Lehner |
31- 89- |
Signs for the Atkin-Lehner involutions |
Class |
85529c |
Isogeny class |
Conductor |
85529 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12240 |
Modular degree for the optimal curve |
Δ |
7612081 = 312 · 892 |
Discriminant |
Eigenvalues |
1 1 3 3 -3 -1 1 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-67,-167] |
[a1,a2,a3,a4,a6] |
Generators |
[-973:671:343] |
Generators of the group modulo torsion |
j |
33874537/7921 |
j-invariant |
L |
12.044457761685 |
L(r)(E,1)/r! |
Ω |
1.6999306193969 |
Real period |
R |
3.5426321599366 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999981833 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85529a1 |
Quadratic twists by: -31 |