Abelian variety isogeny class 1.283.az over $\F_{283}$

• Label: 1.283.az
• Base field: $\F_{283}$
• 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:	$\F_{283}$
Dimension:	$1$
L-polynomial:	$1 - 25 x + 283 x^{2}$
Frobenius angles:	$\pm0.233379450635$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}) \)
Galois group:	$C_2$
Jacobians:	$5$
Isomorphism classes:	5

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$259$	$80031$	$22670788$	$6414404619$	$1815234494269$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$259$	$80031$	$22670788$	$6414404619$	$1815234494269$	$513710715715344$	$145380128282952703$	$41142576380327368275$	$11643349118745789552604$	$3295067800661307805392111$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which 0 are hyperelliptic):

• $y^2=x^3+105 x+210$
• $y^2=x^3+22 x+22$
• $y^2=x^3+52 x+104$
• $y^2=x^3+235 x+235$
• $y^2=x^3+5$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{283}$.

Endomorphism algebra over $\F_{283}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \).

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
1.283.z	$2$	(not in LMFDB)
1.283.ah	$3$	(not in LMFDB)
1.283.bg	$3$	(not in LMFDB)