Atkin-Lehner |
2+ 3- 13- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
83304k |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
599040 |
Modular degree for the optimal curve |
Δ |
-5402944317917952 = -1 · 28 · 311 · 132 · 893 |
Discriminant |
Eigenvalues |
2+ 3- 4 0 0 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-59268,-6584060] |
[a1,a2,a3,a4,a6] |
Generators |
[530:10530:1] |
Generators of the group modulo torsion |
j |
-123372122131456/28950961923 |
j-invariant |
L |
9.1629300086736 |
L(r)(E,1)/r! |
Ω |
0.15111129772596 |
Real period |
R |
1.894905060287 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001522 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27768n1 |
Quadratic twists by: -3 |