Atkin-Lehner |
2+ 3+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
12864h |
Isogeny class |
Conductor |
12864 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-173239488 = -1 · 26 · 32 · 673 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 -4 -4 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1,633] |
[a1,a2,a3,a4,a6] |
Generators |
[8:33:1] [16:67:1] |
Generators of the group modulo torsion |
j |
512/2706867 |
j-invariant |
L |
5.2888133145566 |
L(r)(E,1)/r! |
Ω |
1.4341440610361 |
Real period |
R |
0.61463064256088 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12864m1 6432d1 38592ba1 |
Quadratic twists by: -4 8 -3 |