Abelian variety isogeny class 3.23.ay_kb_acke over $\F_{23}$

• Label: 3.23.ay_kb_acke
• Base field: $\F_{23}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes

Invariants

Base field:	$\F_{23}$
Dimension:	$3$
L-polynomial:	$( 1 - 8 x + 23 x^{2} )^{3}$
	$1 - 24 x + 261 x^{2} - 1616 x^{3} + 6003 x^{4} - 12696 x^{5} + 12167 x^{6}$
Frobenius angles:	$\pm0.186011988595$, $\pm0.186011988595$, $\pm0.186011988595$
Angle rank:	$1$ (numerical)

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$3$
Slopes:	$[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4096$	$134217728$	$1819422502912$	$22087754082942976$	$267251265809157902336$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$0$	$476$	$12288$	$282044$	$6451200$	$148104092$	$3405029376$	$78311048060$	$1801148473344$	$41426476264796$

Jacobians and polarizations

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.ai^3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-7}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
3.23.ai_f_fo	$2$	(not in LMFDB)
3.23.i_f_afo	$2$	(not in LMFDB)
3.23.y_kb_cke	$2$	(not in LMFDB)
3.23.a_a_bo	$3$	(not in LMFDB)