Abelian variety isogeny class 1.53.j over $\F_{53}$

• Label: 1.53.j
• Base field: $\F_{53}$
• 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:	$\F_{53}$
Dimension:	$1$
L-polynomial:	$1 + 9 x + 53 x^{2}$
Frobenius angles:	$\pm0.712106452697$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-131}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$63$	$2835$	$148176$	$7895475$	$418187763$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$63$	$2835$	$148176$	$7895475$	$418187763$	$22164166080$	$1174713305031$	$62259681262275$	$3299763559388688$	$174887471142135675$

Jacobians and polarizations

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

• $y^2=x^3+16 x+16$
• $y^2=x^3+18 x+18$
• $y^2=x^3+46 x+46$
• $y^2=x^3+2 x+4$
• $y^2=x^3+50 x+50$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{53}$.

Endomorphism algebra over $\F_{53}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-131}) \).

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
1.53.aj	$2$	(not in LMFDB)