Atkin-Lehner |
2- 3+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
6864p |
Isogeny class |
Conductor |
6864 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
31104 |
Modular degree for the optimal curve |
Δ |
1647851208548688 = 24 · 318 · 112 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 11- 13- 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-95173,11162788] |
[a1,a2,a3,a4,a6] |
j |
5958673237147648000/102990700534293 |
j-invariant |
L |
1.4229490798248 |
L(r)(E,1)/r! |
Ω |
0.4743163599416 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1716b1 27456bx1 20592be1 75504bg1 |
Quadratic twists by: -4 8 -3 -11 |