Atkin-Lehner |
2- 3- 13+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
53742u |
Isogeny class |
Conductor |
53742 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
479232 |
Modular degree for the optimal curve |
Δ |
-14343913411596288 = -1 · 212 · 34 · 138 · 53 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 -2 13+ 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-81884,-10709232] |
[a1,a2,a3,a4,a6] |
Generators |
[352:1852:1] |
Generators of the group modulo torsion |
j |
-74434516897/17584128 |
j-invariant |
L |
9.187396048626 |
L(r)(E,1)/r! |
Ω |
0.13937035762403 |
Real period |
R |
0.45778286384516 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000085 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
53742f1 |
Quadratic twists by: 13 |