Properties

Label 3.23.ax_jk_acfq
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.144663500024$, $\pm0.186011988595$, $\pm0.268275520367$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4336 137503232 1827473007472 22073623188350976 267076867910104960256 3244957169135969968669184 39472469355019846936115252336 480250837384476815234872348876800 5843209279678578949287087454703881264 71094344483179411944713742576450050588672

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 489 12343 281865 6446996 148072677 3404901809 78310997249 1801152117139 41426508703404

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ai $\times$ 2.23.ap_dx and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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
3.23.ah_e_eo$2$(not in LMFDB)
3.23.h_e_aeo$2$(not in LMFDB)
3.23.x_jk_cfq$2$(not in LMFDB)