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:	$5$
Isomorphism classes:	5

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 contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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)