Properties

Label 3.23.aw_is_acaw
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $1 - 22 x + 226 x^{2} - 1374 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0726497276025$, $\pm0.215791854394$, $\pm0.318152272543$
Angle rank:  $3$ (numerical)
Number field:  6.0.1108002176.1
Galois group:  $S_4\times C_2$

This isogeny class is simple and geometrically 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 it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4558 139593308 1822812807016 21993683946249056 266692352831520365038 3243853199287119272656832 39470552648261328279518346578 480249876007481667892450720029056 5843214445873942394508029117026639384 71094362384835330131654903250949767568988

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 498 12314 280850 6437722 148022304 3404736470 78310840482 1801153709606 41426519134658

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.1108002176.1.
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
3.23.w_is_caw$2$(not in LMFDB)