Abelian variety isogeny class 3.23.f_d_afd over $\F_{23}$

• Label: 3.23.f_d_afd
• Base field: $\F_{23}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{23}$
Dimension:	$3$
L-polynomial:	$1 + 5 x + 3 x^{2} - 133 x^{3} + 69 x^{4} + 2645 x^{5} + 12167 x^{6}$
Frobenius angles:	$\pm0.168713578757$, $\pm0.723478622679$, $\pm0.764357922011$
Angle rank:	$3$ (numerical)
Number field:	6.0.5438813103.1
Galois group:	$S_4\times C_2$
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:	$3$
Slopes:	$[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14757$	$143482311$	$1754657222931$	$22118528422130679$	$266566673041092703047$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$29$	$511$	$11849$	$282435$	$6434689$	$148055047$	$3405090928$	$78310276307$	$1801155094763$	$41426507989531$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 26 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:

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

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 6.0.5438813103.1.

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
3.23.af_d_fd	$2$	(not in LMFDB)