Atkin-Lehner |
2+ 3+ 31- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
8742b |
Isogeny class |
Conductor |
8742 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
146016 |
Modular degree for the optimal curve |
Δ |
-583924786988580864 = -1 · 239 · 36 · 31 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ -1 0 -5 0 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,183222,-20910636] |
[a1,a2,a3,a4,a6] |
j |
680225434775882741591/583924786988580864 |
j-invariant |
L |
0.32024227540771 |
L(r)(E,1)/r! |
Ω |
0.16012113770386 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69936x1 26226y1 |
Quadratic twists by: -4 -3 |