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

• Label: 2.23.s_ex
• Base field: $\F_{23}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{23}$
Dimension:	$2$
L-polynomial:	$( 1 + 9 x + 23 x^{2} )^{2}$
	$1 + 18 x + 127 x^{2} + 414 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.887613658109$, $\pm0.887613658109$
Angle rank:	$1$ (numerical)
Jacobians:	$1$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1089$	$245025$	$150700176$	$78218105625$	$41413896941769$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$42$	$460$	$12384$	$279508$	$6434382$	$148061230$	$3404642514$	$78312048868$	$1801147296672$	$41426535034300$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobian of 1 curve (which is hyperelliptic):

• $y^2=18 x^6+19 x^5+3 x^4+22 x^3+13 x^2+22 x+8$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.j^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.23.as_ex	$2$	(not in LMFDB)
2.23.a_abj	$2$	(not in LMFDB)
2.23.aj_cg	$3$	(not in LMFDB)