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

• Label: 2.23.am_cx
• 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:	$1 - 12 x + 75 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.142553841724$, $\pm0.386281954447$
Angle rank:	$2$ (numerical)
Number field:	4.0.1092112.1
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$317$	$283081$	$149802788$	$78334457401$	$41414845844117$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$12$	$536$	$12312$	$279924$	$6434532$	$148044566$	$3405011916$	$78312028708$	$1801154550600$	$41426502501896$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.1092112.1.

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.m_cx	$2$	(not in LMFDB)