Atkin-Lehner |
2- 3- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696fe |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-8942275584 = -1 · 210 · 38 · 113 |
Discriminant |
Eigenvalues |
2- 3- 2 -2 11+ 0 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-264,-4840] |
[a1,a2,a3,a4,a6] |
Generators |
[38:200:1] |
Generators of the group modulo torsion |
j |
-2048/9 |
j-invariant |
L |
6.9369715591967 |
L(r)(E,1)/r! |
Ω |
0.53799559571659 |
Real period |
R |
3.2235261837653 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001478 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696bb1 17424l1 23232cq1 69696fd1 |
Quadratic twists by: -4 8 -3 -11 |