Properties

Label 3.23.aw_ip_abzu
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:  $1 - 22 x + 223 x^{2} - 1346 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0717686743701$, $\pm0.160639921030$, $\pm0.353689540208$
Angle rank:  $3$ (numerical)
Number field:  6.0.1192782528.1
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
$A(\F_{q^r})$ 4514 137794364 1805875078646 21921181198999344 266559360698935288594 3244070905245034752951644 39472742392793622001634813302 480256653071887456952740347065088 5843223680473010013450927992397349706 71094352946211809253640820466758799848444

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 492 12200 279924 6434512 148032240 3404925358 78311945564 1801156556138 41426513634792

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.1192782528.1.
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_ip_bzu$2$(not in LMFDB)