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

• Label: 2.23.al_ci
• 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:	$1 - 11 x + 60 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.0357805609663$, $\pm0.451061324953$
Angle rank:	$2$ (numerical)
Number field:	4.0.439400.2
Galois group:	$D_{4}$
Jacobians:	$2$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$326$	$278404$	$146701304$	$77803895456$	$41376200585266$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$13$	$529$	$12058$	$278025$	$6428523$	$148031578$	$3404845765$	$78310449969$	$1801148600374$	$41426506081689$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=9x^6+6x^5+9x^4+17x^3+5x^2+7x+15$
• $y^2=21x^6+10x^5+21x^4+9x^3+15x+21$

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 4.0.439400.2.

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.l_ci	$2$	(not in LMFDB)