Atkin-Lehner |
2+ 7+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
32144a |
Isogeny class |
Conductor |
32144 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
20160 |
Modular degree for the optimal curve |
Δ |
-484058810368 = -1 · 211 · 78 · 41 |
Discriminant |
Eigenvalues |
2+ 0 0 7+ 2 1 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1715,43218] |
[a1,a2,a3,a4,a6] |
Generators |
[-49:98:1] |
Generators of the group modulo torsion |
j |
-47250/41 |
j-invariant |
L |
5.3829218563261 |
L(r)(E,1)/r! |
Ω |
0.85353271320315 |
Real period |
R |
1.051106335871 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16072a1 128576bx1 32144e1 |
Quadratic twists by: -4 8 -7 |