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

• Label: 2.23.al_cn
• 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:	$1 - 11 x + 65 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.125643553687$, $\pm0.428178140928$
Angle rank:	$2$ (numerical)
Number field:	4.0.29725.1
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$331$	$284329$	$148717969$	$78130481581$	$41409806217616$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$13$	$539$	$12223$	$279195$	$6433748$	$148058543$	$3405050585$	$78311674819$	$1801152716959$	$41426511980414$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=14x^6+2x^5+x^4+17x^3+15x^2+9x+22$
• $y^2=15x^6+20x^5+20x^4+19x^3+3x^2+18x+7$
• $y^2=20x^6+20x^5+15x^4+3x^3+x^2+10x+21$
• $y^2=21x^6+20x^4+18x^3+2x^2+21x+17$
• $y^2=7x^6+22x^5+14x^4+7x^3+5x^2+8x+9$
• $y^2=10x^6+13x^5+2x^4+10x^3+20x^2+14x+17$

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 4.0.29725.1.

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.l_cn	$2$	(not in LMFDB)