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

• Label: 2.131.abo_ze
• 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:	$1 - 40 x + 654 x^{2} - 5240 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0235496779948$, $\pm0.229984320500$
Angle rank:	$2$ (numerical)
Number field:	4.0.10496.2
Galois group:	$D_{4}$
Jacobians:	$14$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12536$	$289531456$	$5051125076984$	$86730324300637184$	$1488376396692829099576$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$92$	$16870$	$2246852$	$294500334$	$38579473452$	$5053910740246$	$662062559772692$	$86730202464162654$	$11361656642558724092$	$1488377021629244382150$

Jacobians and polarizations

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

• $y^2=127 x^6+112 x^5+121 x^4+73 x^3+104 x^2+124 x+79$
• $y^2=47 x^6+92 x^5+15 x^4+118 x^3+106 x^2+37 x+70$
• $y^2=67 x^6+106 x^5+16 x^4+114 x^3+60 x^2+73 x+75$
• $y^2=18 x^6+82 x^5+73 x^4+73 x^3+119 x^2+125 x+62$
• $y^2=115 x^6+78 x^5+70 x^4+57 x^3+43 x^2+2 x+59$
• $y^2=9 x^6+27 x^5+105 x^4+128 x^3+8 x^2+30 x+124$
• $y^2=67 x^6+65 x^5+19 x^4+115 x^3+78 x^2+74 x+116$
• $y^2=75 x^6+51 x^5+114 x^4+120 x^3+97 x^2+78 x+67$
• $y^2=4 x^6+11 x^5+127 x^4+11 x^3+100 x^2+116 x+30$
• $y^2=96 x^6+76 x^5+43 x^4+125 x^3+55 x^2+29 x+103$
• $y^2=127 x^6+50 x^5+123 x^4+38 x^3+46 x^2+68 x+46$
• $y^2=77 x^6+87 x^5+47 x^4+x^3+43 x^2+119 x+66$
• $y^2=72 x^6+49 x^5+10 x^4+112 x^3+27 x^2+49 x+8$
• $y^2=13 x^6+76 x^5+35 x^4+86 x^3+13 x^2+74 x+101$

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 4.0.10496.2.

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_ze	$2$	(not in LMFDB)