Properties

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

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $( 1 - 5 x + 11 x^{2} )^{3}$
Frobenius angles:  $\pm0.22822922288$, $\pm0.22822922288$, $\pm0.22822922288$
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
$A(\F_{q^r})$ 343 1685159 2582630848 3291326171875 4233994921204433 5569931768213786624 7397215398464534471843 9846286021072917404296875 13108397687134511225731882048 17448991513836070999556906276039

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 113 1452 15341 163227 1774748 19479177 214283861 2357660532 25936814033

Decomposition

1.11.af 3

Base change

This is a primitive isogeny class.