Properties

Label 2.23.an_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:  $1 - 13 x + 81 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0921437596788$, $\pm0.370068381004$
Angle rank:  $2$ (numerical)
Number field:  4.0.488621.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 299 275977 148821569 78211053869 41393392612624 21912447488914801 11593122580108979117 6132683624994648514325 3244157518664321006799311 1716156034070452049005495552

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 523 12233 279483 6431196 148021183 3404909519 78311920131 1801156330649 41426516107518

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.