Atkin-Lehner |
2+ 3+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12168a |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-316180239388416 = -1 · 28 · 39 · 137 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 -4 13+ 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,13689,-593190] |
[a1,a2,a3,a4,a6] |
Generators |
[523:12232:1] |
Generators of the group modulo torsion |
j |
11664/13 |
j-invariant |
L |
3.3318544359298 |
L(r)(E,1)/r! |
Ω |
0.29326730642211 |
Real period |
R |
5.6805759847198 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24336b1 97344i1 12168l1 936f1 |
Quadratic twists by: -4 8 -3 13 |