Atkin-Lehner |
2- 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448bz |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
578290332672 = 210 · 32 · 137 |
Discriminant |
Eigenvalues |
2- 3+ 0 -4 2 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2253,19629] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:169:1] [5:92:1] |
Generators of the group modulo torsion |
j |
256000/117 |
j-invariant |
L |
6.8921422360498 |
L(r)(E,1)/r! |
Ω |
0.82365927937397 |
Real period |
R |
2.0919275751035 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32448w1 8112j1 97344er1 2496w1 |
Quadratic twists by: -4 8 -3 13 |