Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
48672bx |
Isogeny class |
Conductor |
48672 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
319488 |
Modular degree for the optimal curve |
Δ |
-21921829930930176 = -1 · 212 · 38 · 138 |
Discriminant |
Eigenvalues |
2- 3- -3 -2 -2 13+ 3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-26364,7311616] |
[a1,a2,a3,a4,a6] |
Generators |
[338:-6084:1] |
Generators of the group modulo torsion |
j |
-832/9 |
j-invariant |
L |
3.1455301915423 |
L(r)(E,1)/r! |
Ω |
0.32507523256998 |
Real period |
R |
0.4031797714769 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48672bw1 97344fs1 16224k1 48672u1 |
Quadratic twists by: -4 8 -3 13 |