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

• Label: 3.23.av_hv_abue
• 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:	$( 1 - 9 x + 23 x^{2} )( 1 - 12 x + 72 x^{2} - 276 x^{3} + 529 x^{4} )$
	$1 - 21 x + 203 x^{2} - 1200 x^{3} + 4669 x^{4} - 11109 x^{5} + 12167 x^{6}$
Frobenius angles:	$\pm0.0956038575290$, $\pm0.112386341891$, $\pm0.404396142471$
Angle rank:	$2$ (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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4710$	$138332700$	$1790603507160$	$21842027833230000$	$266451776052197536050$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$3$	$495$	$12096$	$278911$	$6431913$	$148048560$	$3405076671$	$78312344591$	$1801156634568$	$41426523123975$

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 $\F_{23^{4}}$.

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.aj $\times$ 2.23.am_cu and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.23.aj : \(\Q(\sqrt{-11}) \).
• 2.23.am_cu : \(\Q(i, \sqrt{10})\).

Endomorphism algebra over $\overline{\F}_{23}$

The base change of $A$ to $\F_{23^{4}}$ is 1.279841.aos^2 $\times$ 1.279841.agl. The endomorphism algebra for each factor is:

• 1.279841.aos^2 : $\mathrm{M}_{2}($\(\Q(\sqrt{-10}) \)$)$
• 1.279841.agl : \(\Q(\sqrt{-11}) \).

Remainder of endomorphism lattice by field

• Endomorphism algebra over $\F_{23^{2}}$
  The base change of $A$ to $\F_{23^{2}}$ is 1.529.abj $\times$ 2.529.a_aos. The endomorphism algebra for each factor is:

  • 1.529.abj : \(\Q(\sqrt{-11}) \).
  • 2.529.a_aos : \(\Q(i, \sqrt{10})\).

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.ad_an_ds	$2$	(not in LMFDB)
3.23.d_an_ads	$2$	(not in LMFDB)
3.23.v_hv_bue	$2$	(not in LMFDB)