Atkin-Lehner |
2+ 3+ 7+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
57288a |
Isogeny class |
Conductor |
57288 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
13184 |
Modular degree for the optimal curve |
Δ |
-3551856 = -1 · 24 · 3 · 7 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ 1 7+ 11+ 1 -6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-140,693] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:31:1] |
Generators of the group modulo torsion |
j |
-19102326016/221991 |
j-invariant |
L |
4.7939223942133 |
L(r)(E,1)/r! |
Ω |
2.5086363134697 |
Real period |
R |
0.47774186800063 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000184 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
114576u1 |
Quadratic twists by: -4 |