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

• Label: 1.283.g
• 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:	$1 + 6 x + 283 x^{2}$
Frobenius angles:	$\pm0.557069938054$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-274}) \)
Galois group:	$C_2$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$290$	$80620$	$22660310$	$6414127200$	$1815234266450$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$290$	$80620$	$22660310$	$6414127200$	$1815234266450$	$513710723280460$	$145380127868953190$	$41142576390307516800$	$11643349119166559596610$	$3295067800662318736485100$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which 0 are hyperelliptic):

• $y^2=x^3+123 x+123$
• $y^2=x^3+265 x+247$
• $y^2=x^3+176 x+176$
• $y^2=x^3+44 x+44$
• $y^2=x^3+169 x+55$
• $y^2=x^3+125 x+250$
• $y^2=x^3+280 x+277$
• $y^2=x^3+266 x+249$
• $y^2=x^3+214 x+214$
• $y^2=x^3+238 x+238$
• $y^2=x^3+268 x+268$
• $y^2=x^3+74 x+74$

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 \(\Q(\sqrt{-274}) \).

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.ag	$2$	(not in LMFDB)