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

• Label: 2.23.am_cv
• 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:	$( 1 - 9 x + 23 x^{2} )( 1 - 3 x + 23 x^{2} )$
	$1 - 12 x + 73 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.112386341891$, $\pm0.398742550628$
Angle rank:	$2$ (numerical)
Jacobians:	$21$
Isomorphism classes:	60
Cyclic group of points:	no
Non-cyclic primes:	$3$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$315$	$280665$	$148916880$	$78177832425$	$41400181590075$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$12$	$532$	$12240$	$279364$	$6432252$	$148040494$	$3405009396$	$78311980036$	$1801154605680$	$41426510261332$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 21 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.aj $\times$ 1.23.ad 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.aj : \(\Q(\sqrt{-11}) \).
• 1.23.ad : \(\Q(\sqrt{-83}) \).

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.ag_t	$2$	(not in LMFDB)
2.23.g_t	$2$	(not in LMFDB)
2.23.m_cv	$2$	(not in LMFDB)