Atkin-Lehner |
2- 7+ 11+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
31724a |
Isogeny class |
Conductor |
31724 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
123648 |
Modular degree for the optimal curve |
Δ |
-2593338997711616 = -1 · 28 · 72 · 117 · 1032 |
Discriminant |
Eigenvalues |
2- 1 1 7+ 11+ 2 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-100805,-12593833] |
[a1,a2,a3,a4,a6] |
j |
-442521399243636736/10130230459811 |
j-invariant |
L |
2.1405757964477 |
L(r)(E,1)/r! |
Ω |
0.13378598727815 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126896m1 |
Quadratic twists by: -4 |