Atkin-Lehner |
2+ 3+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12768b |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1024 |
Modular degree for the optimal curve |
Δ |
178752 = 26 · 3 · 72 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ -2 2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-14,0] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:4:1] |
Generators of the group modulo torsion |
j |
5088448/2793 |
j-invariant |
L |
3.0436345013041 |
L(r)(E,1)/r! |
Ω |
2.6228474878946 |
Real period |
R |
1.1604313690947 |
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 |
12768j1 25536cx1 38304bh1 89376y1 |
Quadratic twists by: -4 8 -3 -7 |