Abelian variety isogeny class 2.131.abn_yp over $\F_{131}$

• Label: 2.131.abn_yp
• Base field: $\F_{131}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{131}$
Dimension:	$2$
L-polynomial:	$1 - 39 x + 639 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.119271920777$, $\pm0.218701635147$
Angle rank:	$2$ (numerical)
Number field:	4.0.2500693.1
Galois group:	$D_{4}$
Jacobians:	$9$

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:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12653$	$290373697$	$5054178837647$	$86738813095974013$	$1488396046016428767248$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16919$	$2248209$	$294529155$	$38579982768$	$5053918463795$	$662062661604255$	$86730203635933843$	$11361656654294522175$	$1488377021730839571974$

Jacobians and polarizations

This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=2x^6+9x^5+2x^4+34x^3+121x^2+103x+42$
• $y^2=94x^6+2x^5+79x^4+22x^3+18x^2+60x+2$
• $y^2=105x^6+90x^5+94x^4+14x^3+2x^2+35x+120$
• $y^2=78x^6+122x^5+5x^4+68x^3+88x^2+30x+93$
• $y^2=121x^6+91x^5+94x^4+27x^3+113x^2+19x+22$
• $y^2=100x^6+94x^5+62x^4+98x^3+3x^2+117x+85$
• $y^2=75x^6+44x^4+7x^3+81x^2+41x+85$
• $y^2=35x^6+43x^5+5x^4+89x^3+46x^2+92x+23$
• $y^2=48x^6+56x^5+38x^4+67x^3+37x^2+17x+129$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{131}$.

Endomorphism algebra over $\F_{131}$

The endomorphism algebra of this simple isogeny class is 4.0.2500693.1.

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
2.131.bn_yp	$2$	(not in LMFDB)