Atkin-Lehner |
2- 3- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
56316o |
Isogeny class |
Conductor |
56316 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-1581906753648 = -1 · 24 · 38 · 133 · 193 |
Discriminant |
Eigenvalues |
2- 3- -4 -2 -2 13- -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-36790,2704529] |
[a1,a2,a3,a4,a6] |
Generators |
[-70:-2223:1] [-187:1755:1] |
Generators of the group modulo torsion |
j |
-50181552673024/14414517 |
j-invariant |
L |
8.772615463887 |
L(r)(E,1)/r! |
Ω |
0.82640734034999 |
Real period |
R |
0.073717811721799 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
56316c1 |
Quadratic twists by: -19 |