Atkin-Lehner |
3- 5+ 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
47685k |
Isogeny class |
Conductor |
47685 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
88128 |
Modular degree for the optimal curve |
Δ |
10358999799885 = 33 · 5 · 11 · 178 |
Discriminant |
Eigenvalues |
0 3- 5+ -1 11+ 2 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-13101,551666] |
[a1,a2,a3,a4,a6] |
Generators |
[-5724:64477:64] |
Generators of the group modulo torsion |
j |
35651584/1485 |
j-invariant |
L |
5.1414820863466 |
L(r)(E,1)/r! |
Ω |
0.71590818852499 |
Real period |
R |
7.1817618079443 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
47685f1 |
Quadratic twists by: 17 |