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

• Label: 1.167.au
• 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:	$1 - 20 x + 167 x^{2}$
Frobenius angles:	$\pm0.218341865198$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-67}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$148$	$27824$	$4659484$	$777847744$	$129892676708$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$148$	$27824$	$4659484$	$777847744$	$129892676708$	$21691966830896$	$3622557575870444$	$604967115872505600$	$101029508512527734068$	$16871927924711259919664$

Jacobians and polarizations

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

• $y^2=x^3+143 x+143$
• $y^2=x^3+124 x+119$
• $y^2=x^3+64 x+64$
• $y^2=x^3+159 x+127$

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 \(\Q(\sqrt{-67}) \).

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.u	$2$	(not in LMFDB)