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

• Label: 2.23.ao_dm
• 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:	$1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.0869454733845$, $\pm0.334554373298$
Angle rank:	$2$ (numerical)
Number field:	4.0.11600.1
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	8

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$284$	$271504$	$148878764$	$78319129856$	$41403008393164$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$10$	$514$	$12238$	$279870$	$6432690$	$148013218$	$3404808886$	$78311602494$	$1801157425594$	$41426529022914$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.11600.1.

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.o_dm	$2$	(not in LMFDB)