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

• Label: 1.283.ac
• 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:	$1 - 2 x + 283 x^{2}$
Frobenius angles:	$\pm0.481067280098$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-282}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$282$	$80652$	$22666878$	$6414092256$	$1815231372042$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$282$	$80652$	$22666878$	$6414092256$	$1815231372042$	$513710744219244$	$145380128902232142$	$41142576380649414528$	$11643349118840863005114$	$3295067800666125473464332$

Jacobians and polarizations

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

• $y^2=x^3+11 x+11$
• $y^2=x^3+108 x+216$
• $y^2=x^3+30 x+60$
• $y^2=x^3+226 x+169$
• $y^2=x^3+163 x+163$
• $y^2=x^3+142 x+1$
• $y^2=x^3+124 x+124$
• $y^2=x^3+89 x+89$

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 \(\Q(\sqrt{-282}) \).

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.c	$2$	(not in LMFDB)