Properties

Label 2.23.an_de
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 4 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.363071407864$
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
$A(\F_{q^r})$ 300 277200 149302800 78309000000 41405518132500 21913449061996800 11593199419917087300 6132693935649204000000 3244158965220313551526800 1716156111853193011023330000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 525 12272 279833 6433081 148027950 3404932087 78312051793 1801157133776 41426517985125

Decomposition

1.23.aj $\times$ 1.23.ae

Base change

This is a primitive isogeny class.