Atkin-Lehner |
2- 5+ 11- 79- |
Signs for the Atkin-Lehner involutions |
Class |
8690f |
Isogeny class |
Conductor |
8690 |
Conductor |
∏ cp |
126 |
Product of Tamagawa factors cp |
deg |
724080 |
Modular degree for the optimal curve |
Δ |
-54439254425600000 = -1 · 221 · 55 · 113 · 792 |
Discriminant |
Eigenvalues |
2- 1 5+ -1 11- -4 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-109275091,439663977121] |
[a1,a2,a3,a4,a6] |
j |
-144306948371105049029627775409/54439254425600000 |
j-invariant |
L |
2.9762726512529 |
L(r)(E,1)/r! |
Ω |
0.21259090366092 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
69520r1 78210r1 43450g1 95590c1 |
Quadratic twists by: -4 -3 5 -11 |