Properties

Label 2.23.ao_do
Base Field $\F_{23}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.135789939707$, $\pm0.314924263207$
Angle rank:  $2$ (numerical)
Number field:  4.0.145728.2
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 286 273988 149920342 78554551504 41436342759526 21914245883188516 11592910729630422478 6132655312170347271168 3244158808782988608111886 1716156537291698793457039588

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 518 12322 280710 6437870 148033334 3404847302 78311558590 1801157046922 41426528254838

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.