Atkin-Lehner |
2- 7- 19- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
50008g |
Isogeny class |
Conductor |
50008 |
Conductor |
∏ cp |
132 |
Product of Tamagawa factors cp |
deg |
371712 |
Modular degree for the optimal curve |
Δ |
-163183809055011584 = -1 · 28 · 711 · 193 · 47 |
Discriminant |
Eigenvalues |
2- -1 -1 7- -2 0 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-94316,22437604] |
[a1,a2,a3,a4,a6] |
Generators |
[102:3724:1] [-192:5782:1] |
Generators of the group modulo torsion |
j |
-362446969457861584/637436754121139 |
j-invariant |
L |
7.78573981419 |
L(r)(E,1)/r! |
Ω |
0.28876527216096 |
Real period |
R |
0.20425890183688 |
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 |
100016c1 |
Quadratic twists by: -4 |