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

• Label: 2.23.an_df
• 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:	$1 - 13 x + 83 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.130958063173$, $\pm0.355407705965$
Angle rank:	$2$ (numerical)
Number field:	4.0.482013.2
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$301$	$278425$	$149784523$	$78405872125$	$41416808880496$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$11$	$527$	$12311$	$280179$	$6434836$	$148032659$	$3404933725$	$78312031891$	$1801157112053$	$41426516286782$

Jacobians and polarizations

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

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

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 4.0.482013.2.

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.n_df	$2$	(not in LMFDB)