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

• Label: 2.23.k_cs
• Base field: $\F_{23}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{23}$
Dimension:	$2$
L-polynomial:	$( 1 + 4 x + 23 x^{2} )( 1 + 6 x + 23 x^{2} )$
	$1 + 10 x + 70 x^{2} + 230 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.636928592136$, $\pm0.715122617226$
Angle rank:	$2$ (numerical)
Jacobians:	$24$
Isomorphism classes:	64

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$840$	$302400$	$143113320$	$78624000000$	$41446149868200$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$34$	$570$	$11758$	$280958$	$6439394$	$148000410$	$3404926958$	$78311161918$	$1801150336354$	$41426517521850$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.e $\times$ 1.23.g and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.23.e : \(\Q(\sqrt{-19}) \).
• 1.23.g : \(\Q(\sqrt{-14}) \).

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.ak_cs	$2$	(not in LMFDB)
2.23.ac_w	$2$	(not in LMFDB)
2.23.c_w	$2$	(not in LMFDB)