Atkin-Lehner |
2+ 3- 5+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
47970g |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12544 |
Modular degree for the optimal curve |
Δ |
-155422800 = -1 · 24 · 36 · 52 · 13 · 41 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 0 -2 13+ 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,30,-604] |
[a1,a2,a3,a4,a6] |
Generators |
[8:6:1] |
Generators of the group modulo torsion |
j |
4019679/213200 |
j-invariant |
L |
4.0169419863015 |
L(r)(E,1)/r! |
Ω |
0.87238000048279 |
Real period |
R |
1.151144565461 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000028 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5330f1 |
Quadratic twists by: -3 |