Atkin-Lehner |
2- 3- 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
47424cy |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-38190849196032 = -1 · 234 · 32 · 13 · 19 |
Discriminant |
Eigenvalues |
2- 3- 2 0 4 13+ 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2497,-302017] |
[a1,a2,a3,a4,a6] |
Generators |
[1108273450:-104359715547:125000] |
Generators of the group modulo torsion |
j |
-6570725617/145686528 |
j-invariant |
L |
9.1726332003984 |
L(r)(E,1)/r! |
Ω |
0.28017020586073 |
Real period |
R |
16.369751330667 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999941 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47424n1 11856z1 |
Quadratic twists by: -4 8 |