Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
32448ba |
Isogeny class |
Conductor |
32448 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-398721024 = -1 · 218 · 32 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -1 -2 -2 13+ -7 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-641,6111] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:96:1] [-5:96:1] |
Generators of the group modulo torsion |
j |
-658489/9 |
j-invariant |
L |
8.9923259635459 |
L(r)(E,1)/r! |
Ω |
1.6913088894306 |
Real period |
R |
0.66459814198797 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32448cc1 507b1 97344be1 32448x1 |
Quadratic twists by: -4 8 -3 13 |