Atkin-Lehner |
2+ 3+ 13- 89- |
Signs for the Atkin-Lehner involutions |
Class |
27768d |
Isogeny class |
Conductor |
27768 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
26880 |
Modular degree for the optimal curve |
Δ |
-48654867456 = -1 · 210 · 35 · 133 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ -3 3 -1 13- 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,448,-10116] |
[a1,a2,a3,a4,a6] |
Generators |
[34:208:1] |
Generators of the group modulo torsion |
j |
9689202428/47514519 |
j-invariant |
L |
3.9680639649031 |
L(r)(E,1)/r! |
Ω |
0.56876783392356 |
Real period |
R |
1.162766166976 |
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 |
55536n1 83304t1 |
Quadratic twists by: -4 -3 |