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

• Label: 2.23.al_co
• 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:	$1 - 11 x + 66 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.138214932321$, $\pm0.422974289955$
Angle rank:	$2$ (numerical)
Number field:	4.0.593393.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$332$	$285520$	$149122448$	$78192507200$	$41414403717172$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$13$	$541$	$12256$	$279417$	$6434463$	$148059694$	$3405057361$	$78311714193$	$1801152390688$	$41426506208661$

Jacobians and polarizations

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

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

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 4.0.593393.1.

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.l_co	$2$	(not in LMFDB)