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

• Label: 2.23.e_bt
• 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:	$1 + 4 x + 45 x^{2} + 92 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.492165033434$, $\pm0.645603365736$
Angle rank:	$2$ (numerical)
Number field:	4.0.170225.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$671$	$321409$	$145623104$	$78092423321$	$41447143748791$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$28$	$604$	$11968$	$279060$	$6439548$	$148037518$	$3404852500$	$78310922724$	$1801149849664$	$41426521925964$

Jacobians and polarizations

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

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

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 4.0.170225.1.

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.ae_bt	$2$	(not in LMFDB)