Abelian variety isogeny class 2.23.aq_ee over $\F_{23}$

• Label: 2.23.aq_ee
• Base field: $\F_{23}$
• 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:	$\F_{23}$
Dimension:	$2$
L-polynomial:	$1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.0613235619868$, $\pm0.259095524151$
Angle rank:	$2$ (numerical)
Number field:	4.0.10496.2
Galois group:	$D_{4}$
Jacobians:	$2$
Isomorphism classes:	2
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$254$	$259588$	$147834350$	$78392460944$	$41427442113454$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$8$	$490$	$12152$	$280134$	$6436488$	$148021930$	$3404702456$	$78310423614$	$1801151744456$	$41426519325450$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 2 curves (of which all are hyperelliptic):

• $y^2=8 x^6+4 x^5+4 x^4+15 x^3+10 x^2+20 x+22$
• $y^2=7 x^6+20 x^5+20 x^4+8 x^3+6 x^2+18 x+5$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The endomorphism algebra of this simple isogeny class is 4.0.10496.2.

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
2.23.q_ee	$2$	(not in LMFDB)