Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
8112be |
Isogeny class |
Conductor |
8112 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
26208 |
Modular degree for the optimal curve |
Δ |
-456704790227712 = -1 · 28 · 37 · 138 |
Discriminant |
Eigenvalues |
2- 3- 2 -1 -2 13+ -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-11717,1134303] |
[a1,a2,a3,a4,a6] |
Generators |
[-113:1014:1] |
Generators of the group modulo torsion |
j |
-851968/2187 |
j-invariant |
L |
5.4390454610096 |
L(r)(E,1)/r! |
Ω |
0.46583757521934 |
Real period |
R |
0.27799621433289 |
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 |
2028a1 32448ck1 24336bu1 8112bf1 |
Quadratic twists by: -4 8 -3 13 |