Atkin-Lehner |
2+ 3- 5+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
47190w |
Isogeny class |
Conductor |
47190 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
163200 |
Modular degree for the optimal curve |
Δ |
-1932902400000 = -1 · 217 · 3 · 55 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -1 11- 13+ -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-69369,-7038308] |
[a1,a2,a3,a4,a6] |
Generators |
[13370783211191592304:-1326008886063647249563:1372330674005383] |
Generators of the group modulo torsion |
j |
-305088363822419089/15974400000 |
j-invariant |
L |
4.7710486578496 |
L(r)(E,1)/r! |
Ω |
0.14708811630679 |
Real period |
R |
32.436669784378 |
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 |
47190cn1 |
Quadratic twists by: -11 |