Atkin-Lehner |
2+ 3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
12768f |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
-6602383872 = -1 · 29 · 36 · 72 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 0 -4 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,352,2856] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:42:1] |
Generators of the group modulo torsion |
j |
9393931000/12895281 |
j-invariant |
L |
3.9241776432466 |
L(r)(E,1)/r! |
Ω |
0.90094376497287 |
Real period |
R |
2.1778149734821 |
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 |
12768t2 25536bl2 38304bn2 89376p2 |
Quadratic twists by: -4 8 -3 -7 |