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

• Label: 2.23.ao_dl
• 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:	$1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.0548738090170$, $\pm0.342656554695$
Angle rank:	$2$ (numerical)
Number field:	4.0.111168.3
Galois group:	$D_{4}$
Jacobians:	$2$
Isomorphism classes:	2

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$283$	$270265$	$148358788$	$78199826425$	$41384994329923$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$10$	$512$	$12196$	$279444$	$6429890$	$147999494$	$3404747342$	$78311263396$	$1801155201148$	$41426516120432$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=19x^6+2x^5+8x^4+10x^3+13x^2+2x+7$
• $y^2=11x^6+17x^5+16x^4+22x^3+22x^2+7x+19$

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 4.0.111168.3.

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_dl	$2$	(not in LMFDB)