Properties

Label 3.11.as_fl_axo
Base Field $\F_{11}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $( 1 - 6 x + 11 x^{2} )^{3}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.140218899004$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 216 1259712 2268747144 3168750108672 4214318118039576 5581968754419000000 7410296971998791645256 9853478099381345260142592 13111095803211447966488930904 17449598901666272811693707765952

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 80 1278 14780 162474 1778576 19513614 214440380 2358145818 25937716880

Decomposition

1.11.ag 3

Base change

This is a primitive isogeny class.