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

• Label: 2.23.f_k
• 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:	$( 1 - 4 x + 23 x^{2} )( 1 + 9 x + 23 x^{2} )$
	$1 + 5 x + 10 x^{2} + 115 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.363071407864$, $\pm0.887613658109$
Angle rank:	$2$ (numerical)
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$660$	$277200$	$151976880$	$78309000000$	$41392898352300$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$29$	$525$	$12488$	$279833$	$6431119$	$148027950$	$3404749153$	$78312051793$	$1801151768984$	$41426517985125$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.ae $\times$ 1.23.j 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.ae : \(\Q(\sqrt{-19}) \).
• 1.23.j : \(\Q(\sqrt{-11}) \).

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.an_de	$2$	(not in LMFDB)
2.23.af_k	$2$	(not in LMFDB)
2.23.n_de	$2$	(not in LMFDB)