Atkin-Lehner |
2- 3+ 5- 13- 41- |
Signs for the Atkin-Lehner involutions |
Class |
47970z |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
108 |
Product of Tamagawa factors cp |
deg |
466560 |
Modular degree for the optimal curve |
Δ |
-91525422231060480 = -1 · 227 · 39 · 5 · 132 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 5- 1 4 13- -4 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,29698,14414221] |
[a1,a2,a3,a4,a6] |
Generators |
[-71:3491:1] |
Generators of the group modulo torsion |
j |
147172862865573/4649973186560 |
j-invariant |
L |
10.977710383256 |
L(r)(E,1)/r! |
Ω |
0.25547947896801 |
Real period |
R |
0.39786156963495 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999902 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47970a1 |
Quadratic twists by: -3 |