Atkin-Lehner |
2- 3- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
10998r |
Isogeny class |
Conductor |
10998 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-1317025589256 = -1 · 23 · 313 · 133 · 47 |
Discriminant |
Eigenvalues |
2- 3- 1 3 -6 13- -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-4037,114117] |
[a1,a2,a3,a4,a6] |
Generators |
[221:3048:1] |
Generators of the group modulo torsion |
j |
-9978645018889/1806619464 |
j-invariant |
L |
7.5610721438393 |
L(r)(E,1)/r! |
Ω |
0.82485646080165 |
Real period |
R |
0.25462585522964 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
87984bn1 3666c1 |
Quadratic twists by: -4 -3 |