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

• Label: 2.23.b_i
• 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:	$1 + x + 8 x^{2} + 23 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.298075176180$, $\pm0.745448442397$
Angle rank:	$2$ (numerical)
Number field:	4.0.816136.1
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	18
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$562$	$288868$	$148586056$	$78851720224$	$41406126802582$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$25$	$545$	$12214$	$281769$	$6433175$	$148014650$	$3404803385$	$78310230769$	$1801155757402$	$41426525897225$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 18 curves (of which all are hyperelliptic):

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

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 4.0.816136.1.

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.ab_i	$2$	(not in LMFDB)