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

• Label: 2.23.am_cs
• 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:	$1 - 12 x + 70 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.0519709137119$, $\pm0.414830815663$
Angle rank:	$2$ (numerical)
Number field:	4.0.7488.1
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	22

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$312$	$277056$	$147591288$	$77934744576$	$41372398716792$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$12$	$526$	$12132$	$278494$	$6427932$	$148021486$	$3404888436$	$78311140798$	$1801150592940$	$41426500509646$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=5x^6+20x^5+12x^4+x^3+3x^2+11x$
• $y^2=11x^6+22x^5+16x^4+x^3+4x^2+10x+22$
• $y^2=10x^6+13x^5+18x^4+5x^3+12x^2+10x+11$
• $y^2=21x^6+11x^5+7x^4+16x^2+21x+22$
• $y^2=7x^6+8x^5+13x^4+15x^3+14x^2+22x+10$
• $y^2=12x^6+22x^5+19x^4+12x^3+21x^2+2x+5$
• $y^2=10x^6+11x^5+14x^4+19x^3+9x^2+13x+21$
• $y^2=3x^6+14x^5+22x^4+5x^3+21x^2+17x+20$
• $y^2=22x^6+18x^5+11x^4+2x^3+5x^2+20x+14$
• $y^2=20x^6+19x^5+2x^4+4x^3+14x^2+16x+22$
• $y^2=7x^6+22x^5+21x^3+12x^2+11x+20$
• $y^2=21x^6+18x^5+19x^4+12x^3+7x^2+13x+10$
• $y^2=13x^5+x^4+18x^3+6x^2+22x+19$
• $y^2=17x^6+17x^5+19x^4+22x^3+7x^2+15x+18$

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 4.0.7488.1.

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.m_cs	$2$	(not in LMFDB)