Abelian variety isogeny class 2.243.acf_bxv over $\F_{3^{5}}$

• Label: 2.243.acf_bxv
• 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

Invariants

Base field:	$\F_{3^{5}}$
Dimension:	$2$
L-polynomial:	$1 - 57 x + 1295 x^{2} - 13851 x^{3} + 59049 x^{4}$
Frobenius angles:	$\pm0.0755542273303$, $\pm0.172748944036$
Angle rank:	$2$ (numerical)
Number field:	4.0.2354677.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$46437$	$3448086561$	$205815094741863$	$12157658268209658621$	$717898822430962619372592$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$187$	$58391$	$14343607$	$3486782339$	$847289594632$	$205891156411091$	$50031545493662521$	$12157665463830575123$	$2954312706590475854185$	$717897987691960932748646$

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 4.0.2354677.1.

Base change

This is a primitive isogeny class.

Twists

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

Twist	Extension degree	Common base change
2.243.cf_bxv	$2$	(not in LMFDB)