Atkin-Lehner |
2+ 3- 17- 29- |
Signs for the Atkin-Lehner involutions |
Class |
47328q |
Isogeny class |
Conductor |
47328 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
-2791272751976448 = -1 · 212 · 314 · 173 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -4 -1 0 -5 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-141665,20632719] |
[a1,a2,a3,a4,a6] |
Generators |
[-395:3888:1] [235:612:1] |
Generators of the group modulo torsion |
j |
-76763457520399936/681463074213 |
j-invariant |
L |
8.6468360267508 |
L(r)(E,1)/r! |
Ω |
0.45558895797023 |
Real period |
R |
0.11297302351949 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47328i1 94656bm1 |
Quadratic twists by: -4 8 |