Properties

Label 2.23.am_dd
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:  $( 1 - 7 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$
Frobenius angles:  $\pm0.23961295769$, $\pm0.325452467839$
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
$A(\F_{q^r})$ 323 290377 152471504 78778408969 41440341210323 21911762784338176 11592371250432470051 6132582088621373586825 3244151363134712287455056 1716156032071680587312299177

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 548 12528 281508 6438492 148016558 3404688852 78310623556 1801152913104 41426516059268

Decomposition

1.23.ah $\times$ 1.23.af

Base change

This is a primitive isogeny class.