Atkin-Lehner |
2+ 3+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
32448t |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
20247552 = 210 · 32 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 -6 13- 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-69,-27] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:8:1] [-4:13:1] |
Generators of the group modulo torsion |
j |
16384/9 |
j-invariant |
L |
5.6464926828516 |
L(r)(E,1)/r! |
Ω |
1.7688930630338 |
Real period |
R |
1.5960525825026 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32448dn1 2028e1 97344de1 32448q1 |
Quadratic twists by: -4 8 -3 13 |