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

• Label: 2.23.al_cl
• 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:	$1 - 11 x + 63 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.0980658819420$, $\pm0.437882154474$
Angle rank:	$2$ (numerical)
Number field:	4.0.2103941.1
Galois group:	$D_{4}$
Jacobians:	$10$
Isomorphism classes:	10
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$329$	$281953$	$147910175$	$78003143309$	$41398488019504$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$13$	$535$	$12157$	$278739$	$6431988$	$148052035$	$3405004231$	$78311416179$	$1801152527011$	$41426519279550$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which all are hyperelliptic):

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

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 4.0.2103941.1.

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.l_cl	$2$	(not in LMFDB)