Atkin-Lehner |
2- 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776x |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
-6435916073216 = -1 · 28 · 710 · 89 |
Discriminant |
Eigenvalues |
2- -3 -3 7- 4 -4 5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1519,-124166] |
[a1,a2,a3,a4,a6] |
Generators |
[546:2401:8] |
Generators of the group modulo torsion |
j |
-12869712/213689 |
j-invariant |
L |
2.7666195952371 |
L(r)(E,1)/r! |
Ω |
0.32298328978807 |
Real period |
R |
2.1414572239428 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999953707 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17444c1 9968p1 |
Quadratic twists by: -4 -7 |