Properties

Label 2.23.aq_eg
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:  $( 1 - 8 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.186011988595$, $\pm0.186011988595$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 256 262144 149035264 78722891776 41490294159616 21921356140773376 11593299228798443776 6132613693309414539264 3244145880938476497899776 1716154866128743486068097024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 494 12248 281310 6446248 148081358 3404961400 78311027134 1801149869384 41426487914414

Decomposition

1.23.ai 2

Base change

This is a primitive isogeny class.