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

• Label: 2.23.e_bx
• 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:	$( 1 + x + 23 x^{2} )( 1 + 3 x + 23 x^{2} )$
	$1 + 4 x + 49 x^{2} + 92 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.533246515430$, $\pm0.601257449372$
Angle rank:	$2$ (numerical)
Jacobians:	$18$
Isomorphism classes:	24
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$675$	$326025$	$145054800$	$77954207625$	$41475478885875$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$28$	$612$	$11920$	$278564$	$6443948$	$148047534$	$3404655044$	$78311072836$	$1801155567280$	$41426504817732$

Jacobians and polarizations

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

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.b $\times$ 1.23.d 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.b : \(\Q(\sqrt{-91}) \).
• 1.23.d : \(\Q(\sqrt{-83}) \).

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.ae_bx	$2$	(not in LMFDB)
2.23.ac_br	$2$	(not in LMFDB)
2.23.c_br	$2$	(not in LMFDB)