Atkin-Lehner |
3- 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
51183f |
Isogeny class |
Conductor |
51183 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
266560 |
Modular degree for the optimal curve |
Δ |
132748701065541 = 313 · 116 · 47 |
Discriminant |
Eigenvalues |
-2 3- 3 3 11- -2 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-13431,227268] |
[a1,a2,a3,a4,a6] |
Generators |
[-112:571:1] |
Generators of the group modulo torsion |
j |
207474688/102789 |
j-invariant |
L |
4.212843395391 |
L(r)(E,1)/r! |
Ω |
0.51814284358242 |
Real period |
R |
4.0653300991842 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000014 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17061e1 423e1 |
Quadratic twists by: -3 -11 |