Properties

Label 2.23.ao_dq
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$
Frobenius angles:  $\pm0.186011988595$, $\pm0.284877382774$
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
$A(\F_{q^r})$ 288 276480 150964128 78785740800 41466087769248 21915788544276480 11592670487988554784 6132584012811573657600 3244149359383039427752992 1716155822942850318659942400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 522 12406 281534 6442490 148043754 3404776742 78310648126 1801151800618 41426511011082

Decomposition

1.23.ai $\times$ 1.23.ag

Base change

This is a primitive isogeny class.