Atkin-Lehner |
2+ 3- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
47658i |
Isogeny class |
Conductor |
47658 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
89856 |
Modular degree for the optimal curve |
Δ |
-2070324569898 = -1 · 2 · 33 · 138 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 0 -4 -3 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-3891,115936] |
[a1,a2,a3,a4,a6] |
j |
-7983625/2538 |
j-invariant |
L |
0.78135482114619 |
L(r)(E,1)/r! |
Ω |
0.78135482149047 |
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 |
47658bc1 |
Quadratic twists by: 13 |