Properties

Label 2.23.ao_dl
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:  $1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0548738090170$, $\pm0.342656554695$
Angle rank:  $2$ (numerical)
Number field:  4.0.111168.3
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 283 270265 148358788 78199826425 41384994329923 21909237111815440 11592570395570841379 6132632195177962461225 3244155484257312398191492 1716156034605534520832062825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 512 12196 279444 6429890 147999494 3404747342 78311263396 1801155201148 41426516120432

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.111168.3.
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_dl$2$(not in LMFDB)