Atkin-Lehner |
2- 3+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
1692b |
Isogeny class |
Conductor |
1692 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
324864 = 28 · 33 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -3 3 1 -4 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24,36] |
[a1,a2,a3,a4,a6] |
Generators |
[0:6:1] |
Generators of the group modulo torsion |
j |
221184/47 |
j-invariant |
L |
2.6460216209599 |
L(r)(E,1)/r! |
Ω |
2.8822110111652 |
Real period |
R |
0.15300878450084 |
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 |
6768i1 27072g1 1692a1 42300b1 |
Quadratic twists by: -4 8 -3 5 |