Atkin-Lehner |
2- 5+ 13+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
69680p |
Isogeny class |
Conductor |
69680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1566720 |
Modular degree for the optimal curve |
Δ |
2451691985126359040 = 216 · 5 · 135 · 674 |
Discriminant |
Eigenvalues |
2- 2 5+ 4 -2 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-523056,-124425280] |
[a1,a2,a3,a4,a6] |
j |
3863751256268453809/598557613556240 |
j-invariant |
L |
3.2287809022417 |
L(r)(E,1)/r! |
Ω |
0.17937671692549 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8710i1 |
Quadratic twists by: -4 |