Properties

Label 2.23.ao_dm
Base Field $\F_{23}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-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:  $D_{4}$
Jacobians:  6

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 6 curves, 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 and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.11600.1.
All geometric endomorphisms are defined over $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.23.o_dm$2$(not in LMFDB)