Properties

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

Learn more about

Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 11 x + 69 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.17408673333$, $\pm0.405448433343$
Angle rank:  $2$ (numerical)
Number field:  4.0.1760213.1
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
$A(\F_{q^r})$ 335 289105 150338285 78372028925 41423951738800 21917435658538105 11593490683307035985 6132656522992838100725 3244147721266737709186955 1716154939750589952863622400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 547 12355 280059 6435948 148054879 3405017629 78311574051 1801150891135 41426489691582

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.