Abelian variety isogeny class 2.167.abv_bic over $\F_{167}$

• Label: 2.167.abv_bic
• Base field: $\F_{167}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{167}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 167 x^{2} )( 1 - 23 x + 167 x^{2} )$
	$1 - 47 x + 886 x^{2} - 7849 x^{3} + 27889 x^{4}$
Frobenius angles:	$\pm0.121023609245$, $\pm0.150776270497$
Angle rank:	$2$ (numerical)
Jacobians:	$0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20880$	$765711360$	$21680589228480$	$604978759744819200$	$16872025292731543532400$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$121$	$27453$	$4655020$	$777811289$	$129892735211$	$21691976571486$	$3622557811912517$	$604967119749389521$	$101029508560558980580$	$16871927925127911821493$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{167}$

The isogeny class factors as 1.167.ay $\times$ 1.167.ax and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.167.ay : \(\Q(\sqrt{-23}) \).
• 1.167.ax : \(\Q(\sqrt{-139}) \).

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
2.167.ab_aik	$2$	(not in LMFDB)
2.167.b_aik	$2$	(not in LMFDB)
2.167.bv_bic	$2$	(not in LMFDB)