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

• Label: 2.23.ao_do
• Base field: $\F_{23}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.135789939707$, $\pm0.314924263207$
Angle rank:	$2$ (numerical)
Number field:	4.0.145728.2
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$286$	$273988$	$149920342$	$78554551504$	$41436342759526$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$10$	$518$	$12322$	$280710$	$6437870$	$148033334$	$3404847302$	$78311558590$	$1801157046922$	$41426528254838$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.145728.2.

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.o_do	$2$	(not in LMFDB)