Atkin-Lehner |
3+ 5+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
78585b |
Isogeny class |
Conductor |
78585 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
33511296 |
Modular degree for the optimal curve |
Δ |
-2.6668458901167E+27 |
Discriminant |
Eigenvalues |
-1 3+ 5+ -2 2 13+ 7 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-193672736,-2692565783692] |
[a1,a2,a3,a4,a6] |
Generators |
[1228152423616741013975801577742181642194275854264418:882341574562413200503157037997250019257220097958140288:2374417703013679594715437281970901346737114701] |
Generators of the group modulo torsion |
j |
-5827679412798973561/19344806796796875 |
j-invariant |
L |
3.0644344633429 |
L(r)(E,1)/r! |
Ω |
0.018622042779747 |
Real period |
R |
82.279761130063 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78585g1 |
Quadratic twists by: 13 |