Atkin-Lehner |
2- 3- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
11952k |
Isogeny class |
Conductor |
11952 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
19968 |
Modular degree for the optimal curve |
Δ |
-24695731650816 = -1 · 28 · 319 · 83 |
Discriminant |
Eigenvalues |
2- 3- 1 2 -3 0 8 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1473,-238102] |
[a1,a2,a3,a4,a6] |
Generators |
[11218:1188162:1] |
Generators of the group modulo torsion |
j |
1893932336/132328809 |
j-invariant |
L |
5.2737004924628 |
L(r)(E,1)/r! |
Ω |
0.32039645387201 |
Real period |
R |
8.2299607700551 |
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 |
2988a1 47808bu1 3984c1 |
Quadratic twists by: -4 8 -3 |