Atkin-Lehner |
2+ 3+ 5+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
67680a |
Isogeny class |
Conductor |
67680 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
35328 |
Modular degree for the optimal curve |
Δ |
296032320 = 26 · 39 · 5 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 -4 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2133,37908] |
[a1,a2,a3,a4,a6] |
Generators |
[52:260:1] |
Generators of the group modulo torsion |
j |
851971392/235 |
j-invariant |
L |
6.2602426746562 |
L(r)(E,1)/r! |
Ω |
1.6886911457996 |
Real period |
R |
3.7071566876418 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000023 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67680s1 67680t1 |
Quadratic twists by: -4 -3 |