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

• Label: 2.23.aq_eg
• Base field: $\F_{23}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{23}$
Dimension:	$2$
L-polynomial:	$( 1 - 8 x + 23 x^{2} )^{2}$
	$1 - 16 x + 110 x^{2} - 368 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.186011988595$, $\pm0.186011988595$
Angle rank:	$1$ (numerical)
Jacobians:	$3$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$256$	$262144$	$149035264$	$78722891776$	$41490294159616$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$8$	$494$	$12248$	$281310$	$6446248$	$148081358$	$3404961400$	$78311027134$	$1801149869384$	$41426487914414$

Jacobians and polarizations

This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=6x^6+10x^5+x^4+21x^3+x^2+10x+6$
• $y^2=4x^6+11x^4+11x^2+4$
• $y^2=14x^6+7x^4+7x^2+14$

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^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$

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
2.23.a_as	$2$	(not in LMFDB)
2.23.q_eg	$2$	(not in LMFDB)
2.23.i_bp	$3$	(not in LMFDB)