Properties

Label 2.23.ap_dw
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.284877382774$
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
$A(\F_{q^r})$ 270 267300 149133960 78532740000 41440524305850 21914298860731200 11592750468002176890 6132624019126759440000 3244156705271078192819880 1716156798949362892960282500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 505 12258 280633 6438519 148033690 3404800233 78311158993 1801155879054 41426534571025

Decomposition

1.23.aj $\times$ 1.23.ag

Base change

This is a primitive isogeny class.