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

• Label: 2.131.abn_yr
• 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:	$1 - 39 x + 641 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.143052069789$, $\pm0.203225231658$
Angle rank:	$2$ (numerical)
Number field:	4.0.460125.1
Galois group:	$D_{4}$
Jacobians:	$12$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12655$	$290444905$	$5054706050305$	$86740889030152605$	$1488401643181213750000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16923$	$2248443$	$294536203$	$38580127848$	$5053920672543$	$662062685755473$	$86730203771647843$	$11361656652821806203$	$1488377021671561368198$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=22x^6+21x^5+89x^4+121x^3+76x^2+127x+26$
• $y^2=53x^6+34x^5+24x^4+21x^3+94x^2+28x+98$
• $y^2=76x^6+33x^5+68x^4+6x^3+59x^2+5x+19$
• $y^2=5x^6+101x^5+64x^4+110x^3+67x^2+12x+26$
• $y^2=126x^6+119x^5+83x^4+112x^3+55x^2+67x+48$
• $y^2=47x^6+110x^5+93x^4+3x^3+2x^2+42x+111$
• $y^2=42x^6+44x^5+100x^4+50x^3+66x^2+115x+79$
• $y^2=95x^6+107x^5+118x^4+21x^3+28x^2+103x+95$
• $y^2=87x^6+55x^5+5x^4+105x^3+31x^2+31x+33$
• $y^2=111x^6+28x^5+115x^4+81x^3+12x^2+16x+120$
• $y^2=72x^6+9x^5+83x^4+32x^3+7x^2+x+90$
• $y^2=72x^6+2x^5+91x^4+x^3+68x^2+95x+96$

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 4.0.460125.1.

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_yr	$2$	(not in LMFDB)