Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
51744bu |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
12 |
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 |
[-169:34364:1] |
Generators of the group modulo torsion |
j |
-19639251778048/3874403907 |
j-invariant |
L |
6.7402466544049 |
L(r)(E,1)/r! |
Ω |
0.18275343553811 |
Real period |
R |
3.0734701076621 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000026 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51744ce1 103488gx1 51744cp1 |
Quadratic twists by: -4 8 -7 |