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

• Label: 2.23.g_cd
• 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:	$( 1 + 3 x + 23 x^{2} )^{2}$
	$1 + 6 x + 55 x^{2} + 138 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.601257449372$, $\pm0.601257449372$
Angle rank:	$1$ (numerical)
Jacobians:	$15$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$729$	$321489$	$143712144$	$78137579961$	$41491852967889$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$30$	$604$	$11808$	$279220$	$6446490$	$148019758$	$3404640486$	$78311911204$	$1801154137824$	$41426485488364$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 15 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.d^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-83}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.23.ag_cd	$2$	(not in LMFDB)
2.23.a_bl	$2$	(not in LMFDB)
2.23.ad_ao	$3$	(not in LMFDB)