Atkin-Lehner |
2- 17+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
68204d |
Isogeny class |
Conductor |
68204 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-22785865136 = -1 · 24 · 176 · 59 |
Discriminant |
Eigenvalues |
2- 1 1 3 2 0 17+ -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-385,7696] |
[a1,a2,a3,a4,a6] |
Generators |
[45:289:1] |
Generators of the group modulo torsion |
j |
-16384/59 |
j-invariant |
L |
9.2336079791658 |
L(r)(E,1)/r! |
Ω |
1.0530812337253 |
Real period |
R |
0.73068183816584 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
236a1 |
Quadratic twists by: 17 |