Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448bo |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-12280707219456 = -1 · 216 · 38 · 134 |
Discriminant |
Eigenvalues |
2+ 3- -3 -4 -4 13+ 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-21857,1247871] |
[a1,a2,a3,a4,a6] |
Generators |
[-165:624:1] [43:-624:1] |
Generators of the group modulo torsion |
j |
-616966948/6561 |
j-invariant |
L |
7.7210022007301 |
L(r)(E,1)/r! |
Ω |
0.71565336088876 |
Real period |
R |
0.11238276888369 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32448cp1 4056c1 97344co1 32448bn1 |
Quadratic twists by: -4 8 -3 13 |