Atkin-Lehner |
2+ 3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
48048y |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
28672 |
Modular degree for the optimal curve |
Δ |
336336 = 24 · 3 · 72 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 2 7- 11+ 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-7007,223440] |
[a1,a2,a3,a4,a6] |
j |
2378274944677888/21021 |
j-invariant |
L |
4.2274770877194 |
L(r)(E,1)/r! |
Ω |
2.1137385439788 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24024u1 |
Quadratic twists by: -4 |