Properties

Label 2.23.ao_dn
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.325452467839$
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
$A(\F_{q^r})$ 285 272745 149399280 78437370825 41420124422925 21912937406173440 11592892715216134845 6132666078284792495625 3244160456331981140841840 1716156696419173852876521225

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 516 12280 280292 6435350 148024494 3404842010 78311696068 1801157961640 41426532096036

Decomposition

1.23.aj $\times$ 1.23.af

Base change

This is a primitive isogeny class.