Abelian variety isogeny class 1.167.at over $\F_{167}$

• Label: 1.167.at
• Base field: $\F_{167}$
• 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:	$\F_{167}$
Dimension:	$1$
L-polynomial:	$1 - 19 x + 167 x^{2}$
Frobenius angles:	$\pm0.237120127213$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-307}) \)
Galois group:	$C_2$
Jacobians:	$3$
Isomorphism classes:	3

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$149$	$27863$	$4660124$	$777851371$	$129892587319$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$149$	$27863$	$4660124$	$777851371$	$129892587319$	$21691963835696$	$3622557528655081$	$604967115486335283$	$101029508514164093108$	$16871927924826823002143$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 3 curves (of which 0 are hyperelliptic):

• $y^2=x^3+21 x+21$
• $y^2=x^3+88 x+88$
• $y^2=x^3+80 x+80$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{167}$.

Endomorphism algebra over $\F_{167}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-307}) \).

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
1.167.t	$2$	(not in LMFDB)