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

• Label: 2.23.ao_dp
• 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:	$1 - 14 x + 93 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.159380640241$, $\pm0.302130010970$
Angle rank:	$2$ (numerical)
Number field:	4.0.82496.2
Galois group:	$D_{4}$
Jacobians:	$5$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$287$	$275233$	$150441956$	$78670674089$	$41451663754207$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$10$	$520$	$12364$	$281124$	$6440250$	$148039750$	$3404825350$	$78311204484$	$1801154916052$	$41426520318600$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which all are hyperelliptic):

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

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 4.0.82496.2.

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_dp	$2$	(not in LMFDB)