Properties

Label 2.243.acf_bxu
Base field $\F_{3^{5}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{3^{5}}$
Dimension:  $2$
L-polynomial:  $1 - 57 x + 1294 x^{2} - 13851 x^{3} + 59049 x^{4}$
Frobenius angles:  $\pm0.0633476822834$, $\pm0.177798504376$
Angle rank:  $2$ (numerical)
Number field:  4.0.749377.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $46436$ $3447965872$ $205812638597072$ $12157631007105115584$ $717898604376423493652876$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $187$ $58389$ $14343436$ $3486774521$ $847289337277$ $205891149605862$ $50031545341577287$ $12157665460889020529$ $2954312706540937526452$ $717897987691243702749909$

Jacobians and polarizations

This isogeny class contains a Jacobian, and hence is principally polarizable.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{3^{5}}$.

Endomorphism algebra over $\F_{3^{5}}$
The endomorphism algebra of this simple isogeny class is 4.0.749377.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.243.cf_bxu$2$(not in LMFDB)