Atkin-Lehner |
2- 3- 5+ 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
19320w |
Isogeny class |
Conductor |
19320 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
319939200000 = 210 · 33 · 55 · 7 · 232 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- -2 -2 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-196936,33572864] |
[a1,a2,a3,a4,a6] |
j |
824899990643380516/312440625 |
j-invariant |
L |
2.3474772502512 |
L(r)(E,1)/r! |
Ω |
0.78249241675039 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38640c1 57960z1 96600d1 |
Quadratic twists by: -4 -3 5 |