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

• Label: 2.131.abn_yj
• 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:	$1 - 39 x + 633 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0557073858855$, $\pm0.244600981273$
Angle rank:	$2$ (numerical)
Number field:	4.0.5504749.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12647$	$290160121$	$5052597291497$	$86732557097001661$	$1488378893455681028912$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16907$	$2247507$	$294507915$	$38579538168$	$5053911364127$	$662062572639561$	$86730202785355939$	$11361656649032432667$	$1488377021732352240902$

Jacobians and polarizations

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

• $y^2=83x^6+36x^5+92x^4+86x^3+4x^2+3x+117$
• $y^2=34x^6+27x^5+35x^4+81x^3+51x^2+117x+41$
• $y^2=54x^6+84x^5+38x^3+74x^2+123x+22$
• $y^2=50x^6+87x^5+101x^4+98x^3+33x^2+108x+10$
• $y^2=46x^6+129x^5+50x^4+42x^3+6x^2+76x+37$
• $y^2=105x^6+45x^5+6x^4+30x^3+98x^2+6x+59$
• $y^2=77x^5+48x^4+100x^3+127x^2+63x+32$
• $y^2=56x^6+104x^5+32x^4+28x^3+74x^2+88x+93$
• $y^2=34x^6+66x^5+101x^4+111x^3+53x^2+29x+68$

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 4.0.5504749.1.

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_yj	$2$	(not in LMFDB)