Abelian variety isogeny class 1.173.u over $\F_{173}$

• Label: 1.173.u
• Base field: $\F_{173}$
• 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:	$\F_{173}$
Dimension:	$1$
L-polynomial:	$1 + 20 x + 173 x^{2}$
Frobenius angles:	$\pm0.774941169793$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-73}) \)
Galois group:	$C_2$
Jacobians:	$4$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$194$	$29876$	$5175338$	$895801984$	$154963164994$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$194$	$29876$	$5175338$	$895801984$	$154963164994$	$26808758023124$	$4637914358419018$	$802359177025190400$	$138808137899851488194$	$24013807852392201294836$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 4 curves (of which 0 are hyperelliptic):

• $y^2=x^3+12 x+12$
• $y^2=x^3+162 x+162$
• $y^2=x^3+118 x+118$
• $y^2=x^3+126 x+126$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-73}) \).

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
1.173.au	$2$	(not in LMFDB)