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

• Label: 1.283.al
• 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:	$1 - 11 x + 283 x^{2}$
Frobenius angles:	$\pm0.393982137132$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-1011}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$273$	$80535$	$22673196$	$6414210075$	$1815229479063$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$273$	$80535$	$22673196$	$6414210075$	$1815229479063$	$513710682947280$	$145380129146222061$	$41142576403448922675$	$11643349118919977778228$	$3295067800659552703961175$

Jacobians and polarizations

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

• $y^2=x^3+151 x+151$
• $y^2=x^3+67 x+67$
• $y^2=x^3+183 x+83$
• $y^2=x^3+82 x+82$
• $y^2=x^3+3 x+3$
• $y^2=x^3+75 x+150$
• $y^2=x^3+42 x+84$
• $y^2=x^3+8 x+16$
• $y^2=x^3+51 x+51$
• $y^2=x^3+117 x+117$
• $y^2=x^3+250 x+250$
• $y^2=x^3+258 x+233$

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 \(\Q(\sqrt{-1011}) \).

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.l	$2$	(not in LMFDB)