Atkin-Lehner |
2- 67- |
Signs for the Atkin-Lehner involutions |
Class |
2144b |
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] |
Generators |
[1:4:1] |
Generators of the group modulo torsion |
j |
-64000/67 |
j-invariant |
L |
2.4206575754049 |
L(r)(E,1)/r! |
Ω |
2.812226399352 |
Real period |
R |
0.43038099207849 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2144a1 4288c1 19296e1 53600b1 |
Quadratic twists by: -4 8 -3 5 |