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

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

Invariants

Base field:	$\F_{23}$
Dimension:	$3$
L-polynomial:	$( 1 - 9 x + 23 x^{2} )^{3}$
	$1 - 27 x + 312 x^{2} - 1971 x^{3} + 7176 x^{4} - 14283 x^{5} + 12167 x^{6}$
Frobenius angles:	$\pm0.112386341891$, $\pm0.112386341891$, $\pm0.112386341891$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3375$	$121287375$	$1754049816000$	$21875648690671875$	$266757296587533703125$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$-3$	$425$	$11844$	$279341$	$6439287$	$148073900$	$3405099849$	$78312580661$	$1801160708652$	$41426546944625$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain 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.aj^3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-11}) \)$)$

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.aj_am_md	$2$	(not in LMFDB)
3.23.j_am_amd	$2$	(not in LMFDB)
3.23.bb_ma_cxv	$2$	(not in LMFDB)
3.23.a_a_aee	$3$	(not in LMFDB)