Properties

Label 2.23.al_co
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:  $1 - 11 x + 66 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.138214932321$, $\pm0.422974289955$
Angle rank:  $2$ (numerical)
Number field:  4.0.593393.1
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
$A(\F_{q^r})$ 332 285520 149122448 78192507200 41414403717172 21918148634794240 11593625968078413668 6132667497681934880000 3244150422185674344138512 1716155623995391255511947600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 541 12256 279417 6434463 148059694 3405057361 78311714193 1801152390688 41426506208661

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.