Properties

Label 3.23.ax_jf_acdz
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:  $1 - 23 x + 239 x^{2} - 1455 x^{3} + 5497 x^{4} - 12167 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.00834882690376$, $\pm0.146501337941$, $\pm0.332481005938$
Angle rank:  $3$ (numerical)
Number field:  6.0.8140239.1
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
$A(\F_{q^r})$ 4259 134367191 1794937674977 21896570024354599 266464474854732220789 3243586226293778010426431 39470904213038541922027933888 480252002295730338688144711687911 5843215984668431085449503414474646483 71094341432463566832133585915640919471911

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 479 12127 279611 6432221 148010123 3404766800 78311187203 1801154183935 41426506925759

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.8140239.1.
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.x_jf_cdz$2$(not in LMFDB)