Properties

Label 2.23.ao_dm
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:  $1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0869454733845$, $\pm0.334554373298$
Angle rank:  $2$ (numerical)
Number field:  4.0.11600.1
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
$A(\F_{q^r})$ 284 271504 148878764 78319129856 41403008393164 21911268418118416 11592779938457273084 6132658750412509466624 3244159490829863598883196 1716156569110414878020587024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 514 12238 279870 6432690 148013218 3404808886 78311602494 1801157425594 41426529022914

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.