Atkin-Lehner |
2- 3+ 13+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
27768i |
Isogeny class |
Conductor |
27768 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
44928 |
Modular degree for the optimal curve |
Δ |
3568474121472 = 28 · 32 · 133 · 893 |
Discriminant |
Eigenvalues |
2- 3+ -2 3 -2 13+ 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4369,-62555] |
[a1,a2,a3,a4,a6] |
Generators |
[91:534:1] |
Generators of the group modulo torsion |
j |
36035394491392/13939352037 |
j-invariant |
L |
4.324349559177 |
L(r)(E,1)/r! |
Ω |
0.60681130576244 |
Real period |
R |
0.59386247395633 |
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 |
55536l1 83304c1 |
Quadratic twists by: -4 -3 |