Atkin-Lehner |
3+ 17+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
13617a |
Isogeny class |
Conductor |
13617 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-29780379 = -1 · 39 · 17 · 89 |
Discriminant |
Eigenvalues |
0 3+ 2 -3 -3 -6 17+ -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-54,-304] |
[a1,a2,a3,a4,a6] |
Generators |
[10:12:1] [18:67:1] |
Generators of the group modulo torsion |
j |
-884736/1513 |
j-invariant |
L |
5.7650213715367 |
L(r)(E,1)/r! |
Ω |
0.83216602427222 |
Real period |
R |
3.4638649039883 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13617b1 |
Quadratic twists by: -3 |