Abelian variety isogeny class 2.157.abv_bhg over $\F_{157}$

• Label: 2.157.abv_bhg
• Base field: $\F_{157}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{157}$
Dimension:	$2$
L-polynomial:	$( 1 - 25 x + 157 x^{2} )( 1 - 22 x + 157 x^{2} )$
	$1 - 47 x + 864 x^{2} - 7379 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0220179720414$, $\pm0.158946998144$
Angle rank:	$2$ (numerical)
Jacobians:	$3$

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18088$	$595818720$	$14960074790752$	$369128775155414400$	$9099051557554290307528$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$111$	$24169$	$3865758$	$607546177$	$95388905091$	$14976072406726$	$2351243282677743$	$369145194338659873$	$57955795538949278646$	$9099059900839552881889$

Jacobians and polarizations

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

• $y^2=22x^6+26x^5+28x^4+123x^3+42x^2+85x+125$
• $y^2=89x^6+87x^5+125x^4+89x^3+143x^2+81x+16$
• $y^2=72x^6+22x^5+83x^4+5x^3+81x^2+100x+114$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The isogeny class factors as 1.157.az $\times$ 1.157.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.157.az : \(\Q(\sqrt{-3}) \).
• 1.157.aw : \(\Q(\sqrt{-1}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.157.ad_ajc	$2$	(not in LMFDB)
2.157.d_ajc	$2$	(not in LMFDB)
2.157.bv_bhg	$2$	(not in LMFDB)
2.157.al_cu	$3$	(not in LMFDB)
2.157.ai_g	$3$	(not in LMFDB)