Atkin-Lehner |
5+ 11+ 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
13585f |
Isogeny class |
Conductor |
13585 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4096 |
Modular degree for the optimal curve |
Δ |
149231225 = 52 · 11 · 134 · 19 |
Discriminant |
Eigenvalues |
-1 2 5+ 2 11+ 13- 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-286,-1886] |
[a1,a2,a3,a4,a6] |
Generators |
[-82:115:8] |
Generators of the group modulo torsion |
j |
2587716619489/149231225 |
j-invariant |
L |
4.1773737298481 |
L(r)(E,1)/r! |
Ω |
1.1650939225898 |
Real period |
R |
1.7927197322266 |
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 |
122265bk1 67925e1 |
Quadratic twists by: -3 5 |