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

• Label: 2.131.abn_yl
• 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:	$1 - 39 x + 635 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0788342236470$, $\pm0.237540823431$
Angle rank:	$2$ (numerical)
Number field:	4.0.6395805.1
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12649$	$290231305$	$5053124458291$	$86734647129520845$	$1488384671153805237904$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16911$	$2247741$	$294515011$	$38579687928$	$5053913809683$	$662062605059403$	$86730203143711411$	$11361656652444533151$	$1488377021762900521926$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=54 x^6+116 x^5+5 x^4+112 x^3+67 x^2+84 x+22$
• $y^2=92 x^6+123 x^5+62 x^4+41 x^3+5 x^2+89 x+87$
• $y^2=89 x^6+94 x^5+77 x^4+4 x^3+104 x^2+78 x+47$
• $y^2=30 x^6+93 x^5+32 x^4+25 x^3+75 x^2+11 x+92$
• $y^2=23 x^6+113 x^5+85 x^4+72 x^3+11 x^2+64 x+44$
• $y^2=22 x^6+44 x^5+67 x^4+93 x^3+29 x^2+107 x+26$
• $y^2=110 x^6+42 x^5+61 x^4+89 x^3+84 x^2+14 x+89$
• $y^2=8 x^6+84 x^5+18 x^4+93 x^3+57 x^2+111 x+118$
• $y^2=x^6+79 x^5+100 x^4+43 x^3+18 x^2+77 x+77$
• $y^2=96 x^6+98 x^5+112 x^4+33 x^3+36 x^2+17 x+27$
• $y^2=21 x^6+127 x^5+79 x^4+129 x^3+7 x^2+107 x+47$
• $y^2=87 x^6+126 x^5+36 x^4+16 x^3+52 x^2+75 x+120$
• $y^2=8 x^6+69 x^5+14 x^4+84 x^3+85 x^2+107 x+44$
• $y^2=18 x^6+67 x^5+112 x^4+114 x^3+110 x^2+52 x+25$
• $y^2=24 x^6+26 x^5+102 x^4+91 x^3+90 x^2+80 x+29$
• $y^2=115 x^6+116 x^5+94 x^4+127 x^3+126 x^2+124 x+23$

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 4.0.6395805.1.

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_yl	$2$	(not in LMFDB)