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

• Label: 2.23.ae_bv
• 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:	$1 - 4 x + 47 x^{2} - 92 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.372788405404$, $\pm0.491106654401$
Angle rank:	$2$ (numerical)
Number field:	4.0.1033488.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$481$	$323713$	$150789652$	$78025515529$	$41392260253201$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$20$	$608$	$12392$	$278820$	$6431020$	$148041974$	$3404887492$	$78310998340$	$1801153173752$	$41426515138688$

Jacobians and polarizations

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

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

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 4.0.1033488.1.

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_bv	$2$	(not in LMFDB)