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

• Label: 2.23.al_cp
• 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:	$1 - 11 x + 67 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.150354367139$, $\pm0.417487041857$
Angle rank:	$2$ (numerical)
Number field:	4.0.2241053.1
Galois group:	$D_{4}$
Jacobians:	$9$
Isomorphism classes:	9
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$333$	$286713$	$149527323$	$78253439229$	$41418293691888$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$13$	$543$	$12289$	$279635$	$6435068$	$148059459$	$3405053819$	$78311704915$	$1801151914531$	$41426500091838$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 9 curves (of which all are hyperelliptic):

• $y^2=18 x^6+18 x^5+14 x^4+14 x^3+17 x^2+15 x+17$
• $y^2=5 x^6+19 x^5+22 x^4+19 x^3+8 x^2+7 x+17$
• $y^2=11 x^6+17 x^4+18 x^3+11 x^2+7 x+20$
• $y^2=x^6+18 x^5+19 x^4+20 x^3+17 x^2+3 x+14$
• $y^2=15 x^6+21 x^5+22 x^4+2 x^3+6 x^2+4 x+9$
• $y^2=11 x^6+13 x^5+x^4+15 x^3+22 x^2+17$
• $y^2=13 x^6+10 x^5+13 x^4+4 x^3+16 x+1$
• $y^2=15 x^6+4 x^5+3 x^4+13 x^3+6 x^2+10 x+10$
• $y^2=7 x^6+22 x^5+12 x^4+12 x^3+14 x^2+21 x+2$

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 4.0.2241053.1.

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_cp	$2$	(not in LMFDB)