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

• Label: 2.131.abo_zf
• Base field: $\F_{131}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 40 x + 655 x^{2} - 5240 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0466407159379$, $\pm0.226116217998$
Angle rank:	$2$ (numerical)
Number field:	4.0.1951376.2
Galois group:	$D_{4}$
Jacobians:	$14$

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12537$	$289567089$	$5051395452852$	$86731438253156361$	$1488379652824765432977$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$16872$	$2246972$	$294504116$	$38579557852$	$5053912233102$	$662062581979492$	$86730202754371108$	$11361656646057913412$	$1488377021670874991352$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=92x^6+92x^5+51x^4+58x^3+43x^2+93x+107$
• $y^2=56x^6+35x^5+80x^4+20x^3+49x^2+107x+124$
• $y^2=75x^6+121x^5+44x^4+52x^3+97x^2+61x+96$
• $y^2=120x^6+68x^5+87x^4+93x^3+104x^2+93x+119$
• $y^2=32x^6+130x^5+100x^4+61x^3+53x^2+10x+84$
• $y^2=78x^6+125x^5+8x^4+109x^3+107x^2+7x+113$
• $y^2=49x^6+49x^5+19x^4+14x^3+106x^2+61x+47$
• $y^2=69x^6+62x^5+84x^4+99x^3+49x^2+114x+43$
• $y^2=105x^6+89x^5+79x^4+58x^3+56x^2+90x+112$
• $y^2=8x^6+75x^5+61x^4+51x^3+39x^2+46x+120$
• $y^2=13x^6+40x^5+116x^4+92x^3+95x^2+110x+56$
• $y^2=65x^6+61x^5+42x^4+43x^3+5x^2+68x+51$
• $y^2=47x^6+41x^5+46x^4+7x^3+54x^2+10x+115$
• $y^2=110x^6+14x^5+130x^4+59x^3+79x^2+12x+47$

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 4.0.1951376.2.

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_zf	$2$	(not in LMFDB)