Properties

Label 2.23.am_cs
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:  $1 - 12 x + 70 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0519709137119$, $\pm0.414830815663$
Angle rank:  $2$ (numerical)
Number field:  4.0.7488.1
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
$A(\F_{q^r})$ 312 277056 147591288 77934744576 41372398716792 21912492430550592 11593050789098338872 6132622594404614750208 3244147184171830704254136 1716155387905118298314020416

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 526 12132 278494 6427932 148021486 3404888436 78311140798 1801150592940 41426500509646

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.