Atkin-Lehner |
2- 3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
48048ct |
Isogeny class |
Conductor |
48048 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-9299017728 = -1 · 214 · 34 · 72 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 11+ 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-624,7380] |
[a1,a2,a3,a4,a6] |
Generators |
[12:-42:1] |
Generators of the group modulo torsion |
j |
-6570725617/2270268 |
j-invariant |
L |
6.3500877794726 |
L(r)(E,1)/r! |
Ω |
1.2227973132098 |
Real period |
R |
0.64913535862317 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006s1 |
Quadratic twists by: -4 |