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

• Label: 2.23.ae_bw
• 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:	$1 - 4 x + 48 x^{2} - 92 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.384155169532$, $\pm0.480547927870$
Angle rank:	$2$ (numerical)
Number field:	4.0.471296.1
Galois group:	$D_{4}$
Jacobians:	$12$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$482$	$324868$	$150939746$	$77990411024$	$41385055791682$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$20$	$610$	$12404$	$278694$	$6429900$	$148044610$	$3404939180$	$78311036094$	$1801151616692$	$41426510446050$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

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

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 4.0.471296.1.

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.e_bw	$2$	(not in LMFDB)