Properties

Label 2.23.al_cm
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 2 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.433137181604$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 330 283140 148313880 78067360800 41404501035150 21917600935813440 11593543119040321230 6132656857338591465600 3244151151725578741029240 1716156055261745420101049700

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 537 12190 278969 6432923 148055994 3405033029 78311578321 1801152795730 41426516619057

Decomposition

1.23.aj $\times$ 1.23.ac

Base change

This is a primitive isogeny class.