Atkin-Lehner |
2- 3- 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12768w |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
312874809408 = 26 · 37 · 76 · 19 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ -6 6 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-13622,-615912] |
[a1,a2,a3,a4,a6] |
Generators |
[-68:24:1] |
Generators of the group modulo torsion |
j |
4368157081239232/4888668897 |
j-invariant |
L |
6.1320001279875 |
L(r)(E,1)/r! |
Ω |
0.44194259586993 |
Real period |
R |
1.9821579238353 |
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 |
12768q1 25536ca1 38304k1 89376ca1 |
Quadratic twists by: -4 8 -3 -7 |