Atkin-Lehner |
2- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
2144a |
Isogeny class |
Conductor |
2144 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
288 |
Modular degree for the optimal curve |
Δ |
-274432 = -1 · 212 · 67 |
Discriminant |
Eigenvalues |
2- 2 0 -4 2 -2 7 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-13,-27] |
[a1,a2,a3,a4,a6] |
j |
-64000/67 |
j-invariant |
L |
2.398426669031 |
L(r)(E,1)/r! |
Ω |
1.1992133345155 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2144b1 4288e1 19296c1 53600h1 |
Quadratic twists by: -4 8 -3 5 |