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

• Label: 2.131.abo_zh
• 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:	$1 - 40 x + 657 x^{2} - 5240 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0763285075711$, $\pm0.217235058532$
Angle rank:	$2$ (numerical)
Number field:	4.0.154025.2
Galois group:	$D_{4}$
Jacobians:	$20$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12539$	$289638361$	$5051936216384$	$86733662634214025$	$1488386118798410092579$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$16876$	$2247212$	$294511668$	$38579725452$	$5053915156006$	$662062624099892$	$86730203269285668$	$11361656651501069012$	$1488377021722282560156$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=120x^6+75x^5+41x^4+28x^3+85x^2+113x+36$
• $y^2=61x^6+130x^5+27x^4+9x^3+118x^2+8x+110$
• $y^2=18x^6+112x^5+94x^4+88x^3+48x^2+50x+38$
• $y^2=60x^6+78x^5+123x^4+104x^3+3x^2+59x+66$
• $y^2=61x^6+89x^5+57x^4+104x^3+64x^2+90x+21$
• $y^2=53x^6+47x^5+32x^4+63x^3+86x^2+115x+46$
• $y^2=119x^6+126x^5+120x^4+110x^3+116x^2+15x+69$
• $y^2=41x^6+20x^5+38x^4+31x^3+11x^2+108x+98$
• $y^2=84x^6+89x^5+68x^4+129x^3+70x^2+109x+117$
• $y^2=97x^6+69x^5+76x^4+109x^3+64x^2+93x+37$
• $y^2=96x^6+12x^5+65x^4+112x^3+97x^2+25x+71$
• $y^2=18x^6+9x^5+88x^4+47x^3+45x^2+126x+82$
• $y^2=76x^6+85x^5+28x^4+108x^3+61x^2+15x+52$
• $y^2=113x^6+82x^5+82x^4+109x^3+27x^2+115x+6$
• $y^2=97x^6+128x^5+98x^4+54x^3+118x^2+116x+91$
• $y^2=26x^6+40x^5+124x^4+42x^3+100x^2+34x+55$
• $y^2=31x^6+78x^5+92x^4+60x^3+129x^2+99x+96$
• $y^2=25x^6+2x^5+78x^4+78x^3+17x^2+55x+8$
• $y^2=111x^6+86x^5+48x^4+30x^3+49x^2+38x+50$
• $y^2=50x^6+97x^5+30x^4+3x^3+109x^2+119x+126$

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 4.0.154025.2.

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.bo_zh	$2$	(not in LMFDB)