Atkin-Lehner |
2- 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744ce |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
1467648 |
Modular degree for the optimal curve |
Δ |
-9.1484846151588E+19 |
Discriminant |
Eigenvalues |
2- 3- 2 7+ 11+ -1 8 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1612557,-913217733] |
[a1,a2,a3,a4,a6] |
Generators |
[17082:586971:8] |
Generators of the group modulo torsion |
j |
-19639251778048/3874403907 |
j-invariant |
L |
8.8820326655663 |
L(r)(E,1)/r! |
Ω |
0.066281633307126 |
Real period |
R |
1.5952908647277 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999809 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744bu1 103488ez1 51744bz1 |
Quadratic twists by: -4 8 -7 |