Atkin-Lehner |
2- 3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
12768o |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10240 |
Modular degree for the optimal curve |
Δ |
14478912 = 26 · 35 · 72 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -2 4 8 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6158,-183960] |
[a1,a2,a3,a4,a6] |
j |
403583419000000/226233 |
j-invariant |
L |
2.1557270065881 |
L(r)(E,1)/r! |
Ω |
0.53893175164702 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12768u1 25536db2 38304u1 89376cj1 |
Quadratic twists by: -4 8 -3 -7 |