Properties

Label 2.23.am_cv
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 3 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.398742550628$
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
$A(\F_{q^r})$ 315 280665 148916880 78177832425 41400181590075 21915306183133440 11593462650638869035 6132688316249673249225 3244154411726693360436240 1716155791883303691727092825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 532 12240 279364 6432252 148040494 3405009396 78311980036 1801154605680 41426510261332

Decomposition

1.23.aj $\times$ 1.23.ad

Base change

This is a primitive isogeny class.