Properties

Label 2.23.an_di
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$
Frobenius angles:  $\pm0.186011988595$, $\pm0.325452467839$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 304 282112 151232704 78690064384 41445675302224 21914426997170176 11592812734221129232 6132626071695232819200 3244153110435448682059456 1716155720412719589175946752

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 533 12428 281193 6439321 148034558 3404818519 78311185201 1801153883204 41426508536093

Decomposition

1.23.ai $\times$ 1.23.af

Base change

This is a primitive isogeny class.