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

• Label: 2.243.acb_bsz
• 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:	$1 - 53 x + 1169 x^{2} - 12879 x^{3} + 59049 x^{4}$
Frobenius angles:	$\pm0.0434068874004$, $\pm0.249029527486$
Angle rank:	$2$ (numerical)
Number field:	4.0.51445933.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$47287$	$3459091337$	$205867548643009$	$12157725179238206269$	$717897896262439068938672$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$191$	$58579$	$14347265$	$3486801531$	$847288501536$	$205891113003607$	$50031544530940779$	$12157665448866037379$	$2954312706435275657921$	$717897987691452440736934$

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 4.0.51445933.1.

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.cb_bsz	$2$	(not in LMFDB)