Atkin-Lehner |
2- 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360ce |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-71792854228080 = -1 · 24 · 37 · 5 · 177 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 3 1 -2 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,8574,-272709] |
[a1,a2,a3,a4,a6] |
j |
180472064/185895 |
j-invariant |
L |
1.3351770457654 |
L(r)(E,1)/r! |
Ω |
0.3337942581768 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17340n1 4080bf1 |
Quadratic twists by: -4 17 |