Properties

Label 2.23.ao_dr
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.23961295769$, $\pm0.23961295769$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 289 277729 151486864 78899753881 41479615178089 21916026354309376 11592416240980755049 6132525727654696260969 3244142386345732416264976 1716155489446411799503060849

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 524 12448 281940 6444590 148045358 3404702066 78309903844 1801147929184 41426502960764

Decomposition

1.23.ah 2

Base change

This is a primitive isogeny class.