Atkin-Lehner |
2+ 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448l |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-292032 = -1 · 26 · 33 · 132 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -3 2 13+ 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,9,-27] |
[a1,a2,a3,a4,a6] |
Generators |
[84:125:27] |
Generators of the group modulo torsion |
j |
6656/27 |
j-invariant |
L |
5.9878877688884 |
L(r)(E,1)/r! |
Ω |
1.5588988756087 |
Real period |
R |
3.8411008325029 |
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 |
32448bq1 16224x1 97344cz1 32448m1 |
Quadratic twists by: -4 8 -3 13 |