Abelian variety isogeny class 1.223.m over $\F_{223}$

• Label: 1.223.m
• Base field: $\F_{223}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{223}$
Dimension:	$1$
L-polynomial:	$1 + 12 x + 223 x^{2}$
Frobenius angles:	$\pm0.631611723184$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-187}) \)
Galois group:	$C_2$
Jacobians:	$8$
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:	$1$
Slopes:	$[0, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$236$	$50032$	$11083268$	$2472981696$	$551474383196$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$236$	$50032$	$11083268$	$2472981696$	$551474383196$	$122978478736624$	$27424204582115444$	$6115597644769198848$	$1363778273655323663564$	$304122555033556156648432$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):

• $y^2=x^3+138 x+191$
• $y^2=x^3+99 x+99$
• $y^2=x^3+156 x+22$
• $y^2=x^3+59 x+177$
• $y^2=x^3+219 x+211$
• $y^2=x^3+61 x+61$
• $y^2=x^3+127 x+127$
• $y^2=x^3+148 x+221$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{223}$.

Endomorphism algebra over $\F_{223}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-187}) \).

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
1.223.am	$2$	(not in LMFDB)