Atkin-Lehner |
2- 3+ 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
47424cp |
Isogeny class |
Conductor |
47424 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-2962729795584 = -1 · 216 · 3 · 133 · 193 |
Discriminant |
Eigenvalues |
2- 3+ -1 -3 -2 13- -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10561,429409] |
[a1,a2,a3,a4,a6] |
Generators |
[45:208:1] [-67:912:1] |
Generators of the group modulo torsion |
j |
-1987925163844/45207669 |
j-invariant |
L |
7.0261303694083 |
L(r)(E,1)/r! |
Ω |
0.8015206863413 |
Real period |
R |
0.2435000011416 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47424bs1 11856i1 |
Quadratic twists by: -4 8 |