Atkin-Lehner |
2+ 3- 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
83304c |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
359424 |
Modular degree for the optimal curve |
Δ |
2601417634553088 = 28 · 38 · 133 · 893 |
Discriminant |
Eigenvalues |
2+ 3- 2 3 2 13+ -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-39324,1728308] |
[a1,a2,a3,a4,a6] |
j |
36035394491392/13939352037 |
j-invariant |
L |
3.3230478115648 |
L(r)(E,1)/r! |
Ω |
0.41538097995262 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27768i1 |
Quadratic twists by: -3 |