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

• Label: 2.131.abp_bad
• 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:	$1 - 41 x + 679 x^{2} - 5371 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0723194931602$, $\pm0.195750322624$
Angle rank:	$2$ (numerical)
Number field:	4.0.783653.1
Galois group:	$D_{4}$
Jacobians:	$13$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12429$	$289011537$	$5050505394639$	$86731838853806493$	$1488385759381050385584$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$91$	$16839$	$2246575$	$294505475$	$38579716136$	$5053916054835$	$662062643309249$	$86730203491637203$	$11361656652577246489$	$1488377021704920979974$

Jacobians and polarizations

This isogeny class contains the Jacobians of 13 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=77x^6+37x^5+64x^4+38x^3+81x^2+19x+94$
• $y^2=116x^6+115x^5+27x^4+73x^3+130x^2+128x+14$
• $y^2=21x^6+95x^5+126x^4+55x^3+41x^2+94x+15$
• $y^2=103x^6+66x^5+62x^4+29x^3+125x^2+16x+22$
• $y^2=113x^6+15x^5+62x^4+38x^3+62x^2+115x+72$
• $y^2=96x^6+64x^5+5x^4+113x^3+115x^2+10x+72$
• $y^2=89x^6+108x^5+31x^4+47x^3+29x^2+89x+57$
• $y^2=115x^6+95x^5+51x^4+6x^3+110x^2+116x+14$
• $y^2=62x^6+72x^5+113x^4+51x^3+108x^2+8x+48$
• $y^2=67x^6+33x^5+7x^4+29x^3+53x^2+123x+80$
• $y^2=48x^6+64x^5+33x^4+14x^3+124x^2+75x+23$
• $y^2=117x^6+35x^5+41x^4+71x^3+17x^2+127x+56$
• $y^2=111x^6+13x^5+93x^4+112x^3+72x^2+125x+122$

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 4.0.783653.1.

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.bp_bad	$2$	(not in LMFDB)