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

• Label: 2.23.am_cy
• 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:	$1 - 12 x + 76 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.156924629149$, $\pm0.379300706967$
Angle rank:	$2$ (numerical)
Number field:	4.0.942336.2
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$318$	$284292$	$150246414$	$78411145104$	$41421021299598$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$12$	$538$	$12348$	$280198$	$6435492$	$148044058$	$3404991252$	$78311930686$	$1801154110284$	$41426498189818$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.942336.2.

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.m_cy	$2$	(not in LMFDB)