Atkin-Lehner |
2- 3+ 37+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
83472k |
Isogeny class |
Conductor |
83472 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
718080 |
Modular degree for the optimal curve |
Δ |
41037890320358352 = 24 · 322 · 37 · 472 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 -4 6 -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-86293,479224] |
[a1,a2,a3,a4,a6] |
j |
4441559302930432000/2564868145022397 |
j-invariant |
L |
0.30787937466726 |
L(r)(E,1)/r! |
Ω |
0.30787944378917 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20868a1 |
Quadratic twists by: -4 |