Properties

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

Learn more about

Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 12 x + 75 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.142553841724$, $\pm0.386281954447$
Angle rank:  $2$ (numerical)
Number field:  4.0.1092112.1
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
$A(\F_{q^r})$ 317 283081 149802788 78334457401 41414845844117 21915908799150352 11593471230482002997 6132692127827689929513 3244154312521519205850596 1716155470437059525838520441

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 536 12312 279924 6434532 148044566 3405011916 78312028708 1801154550600 41426502501896

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.