Properties

Label 2.23.as_ex
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:  $( 1 - 9 x + 23 x^{2} )^{2}$
Frobenius angles:  $\pm0.112386341891$, $\pm0.112386341891$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 225 245025 145443600 78218105625 41439153155625 21918376118073600 11593459198053117225 6132693706588016555625 3244160572715434839699600 1716156818141235393219800625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 460 11952 279508 6438306 148061230 3405008382 78312048868 1801158026256 41426535034300

Decomposition

1.23.aj 2

Base change

This is a primitive isogeny class.