Properties

Label 2.23.ar_eo
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.186011988595$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 240 253440 147228480 78470092800 41464715773200 21919866078781440 11593379213149866960 6132653699818223001600 3244153226818638848696640 1716155842134711904186867200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 477 12100 280409 6442277 148071294 3404984891 78311538001 1801153947820 41426511474357

Decomposition

1.23.aj $\times$ 1.23.ai

Base change

This is a primitive isogeny class.