Properties

Label 2.23.am_da
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 4 x + 23 x^{2} )$
Frobenius angles:  $\pm0.186011988595$, $\pm0.363071407864$
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
$A(\F_{q^r})$ 320 286720 151135040 78561280000 41431060001600 21914938687774720 11593119436806082880 6132653928877916160000 3244151619327157483085120 1716155135847071199581593600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 542 12420 280734 6437052 148038014 3404908596 78311540926 1801153055340 41426494425182

Decomposition

1.23.ai $\times$ 1.23.ae

Base change

This is a primitive isogeny class.