Atkin-Lehner |
2+ 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448d |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-120777273274941504 = -1 · 26 · 34 · 1312 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 -2 13+ 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-105512,-21262710] |
[a1,a2,a3,a4,a6] |
Generators |
[4081683792396490:151255759712869825:2802028309192] |
Generators of the group modulo torsion |
j |
-420526439488/390971529 |
j-invariant |
L |
5.1311723350714 |
L(r)(E,1)/r! |
Ω |
0.12756600390735 |
Real period |
R |
20.111833003714 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32448bd1 16224u2 97344cf1 2496f1 |
Quadratic twists by: -4 8 -3 13 |