Atkin-Lehner |
3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12675k |
Isogeny class |
Conductor |
12675 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
48384 |
Modular degree for the optimal curve |
Δ |
-14706683671875 = -1 · 3 · 57 · 137 |
Discriminant |
Eigenvalues |
2 3+ 5+ -3 5 13+ -5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1408,-185157] |
[a1,a2,a3,a4,a6] |
Generators |
[618:3207:8] |
Generators of the group modulo torsion |
j |
-4096/195 |
j-invariant |
L |
7.2556945383187 |
L(r)(E,1)/r! |
Ω |
0.30752620061328 |
Real period |
R |
2.9492180356703 |
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 |
38025bu1 2535h1 975b1 |
Quadratic twists by: -3 5 13 |