Atkin-Lehner |
2- 3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48048ca |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
44890343866368 = 224 · 35 · 7 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ 11+ 13+ 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-892232,-324685452] |
[a1,a2,a3,a4,a6] |
Generators |
[-68245:774:125] |
Generators of the group modulo torsion |
j |
19177749277229260873/10959556608 |
j-invariant |
L |
8.3358938587366 |
L(r)(E,1)/r! |
Ω |
0.15533884804398 |
Real period |
R |
5.3662647584267 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006g1 |
Quadratic twists by: -4 |