Properties

Label 2.23.ao_dl
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:  $1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.054873809017$, $\pm0.342656554695$
Angle rank:  $2$ (numerical)
Number field:  4.0.111168.3
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
$A(\F_{q^r})$ 283 270265 148358788 78199826425 41384994329923 21909237111815440 11592570395570841379 6132632195177962461225 3244155484257312398191492 1716156034605534520832062825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 512 12196 279444 6429890 147999494 3404747342 78311263396 1801155201148 41426516120432

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.