Atkin-Lehner |
2- 3- 23- 47- |
Signs for the Atkin-Lehner involutions |
Class |
51888z |
Isogeny class |
Conductor |
51888 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-276177604313088 = -1 · 226 · 34 · 23 · 472 |
Discriminant |
Eigenvalues |
2- 3- -2 2 2 -2 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-31464,-2302668] |
[a1,a2,a3,a4,a6] |
Generators |
[4812:333606:1] |
Generators of the group modulo torsion |
j |
-841045259316457/67426172928 |
j-invariant |
L |
7.2193413238083 |
L(r)(E,1)/r! |
Ω |
0.178412174645 |
Real period |
R |
5.0580498066969 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6486d1 |
Quadratic twists by: -4 |