Atkin-Lehner |
2- 3- 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
27768k |
Isogeny class |
Conductor |
27768 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
-225120330444552192 = -1 · 211 · 39 · 137 · 89 |
Discriminant |
Eigenvalues |
2- 3- 2 -3 -2 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-703472,-228479712] |
[a1,a2,a3,a4,a6] |
Generators |
[18547:2523306:1] |
Generators of the group modulo torsion |
j |
-18799003355779763426/109922036349879 |
j-invariant |
L |
6.5831081598995 |
L(r)(E,1)/r! |
Ω |
0.082395975402487 |
Real period |
R |
8.8773324017108 |
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 |
55536b1 83304h1 |
Quadratic twists by: -4 -3 |