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

• Label: 1.283.b
• 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:	$1 + x + 283 x^{2}$
Frobenius angles:	$\pm0.509462172837$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-1131}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$285$	$80655$	$22664340$	$6414088875$	$1815232560675$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$285$	$80655$	$22664340$	$6414088875$	$1815232560675$	$513710746356240$	$145380128436289185$	$41142576379585369875$	$11643349119007999129740$	$3295067800666589719043775$

Jacobians and polarizations

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

• $y^2=x^3+58 x+58$
• $y^2=x^3+5 x+10$
• $y^2=x^3+270 x+270$
• $y^2=x^3+156 x+29$
• $y^2=x^3+83 x+83$
• $y^2=x^3+48 x+48$
• $y^2=x^3+170 x+57$
• $y^2=x^3+236 x+236$

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 \(\Q(\sqrt{-1131}) \).

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
1.283.ab	$2$	(not in LMFDB)