Atkin-Lehner |
2- 3- 7+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
31584w |
Isogeny class |
Conductor |
31584 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
5050092096 = 26 · 36 · 72 · 472 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ -4 2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-862,8840] |
[a1,a2,a3,a4,a6] |
Generators |
[38:180:1] |
Generators of the group modulo torsion |
j |
1108075264192/78907689 |
j-invariant |
L |
7.5175266209985 |
L(r)(E,1)/r! |
Ω |
1.3372390774544 |
Real period |
R |
1.8738924469435 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
31584r1 63168by2 94752j1 |
Quadratic twists by: -4 8 -3 |