Properties

Label 3.23.aw_is_acax
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:  $1 - 22 x + 226 x^{2} - 1375 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0527001661086$, $\pm0.227767494529$, $\pm0.313634986415$
Angle rank:  $3$ (numerical)
Number field:  6.0.651528243.1
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
$A(\F_{q^r})$ 4557 139567239 1822286102553 21986705596018779 266638895595308819247 3243579938145113146735743 39469541552566786342430931693 480247114772583627424736085624627 5843209134077744319625892429755651392 71094356552824358812240542221662732488879

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 498 12311 280762 6436432 148009833 3404649250 78310390226 1801152072260 41426515736358

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.651528243.1.
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_cax$2$(not in LMFDB)