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

• Label: 2.131.abn_yi
• 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:	$1 - 39 x + 632 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0409844205625$, $\pm0.247789329099$
Angle rank:	$2$ (numerical)
Number field:	4.0.3751992.1
Galois group:	$D_{4}$
Jacobians:	$8$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12646$	$290124532$	$5052333713800$	$86731510318365600$	$1488375982039853925706$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16905$	$2247390$	$294504361$	$38579462703$	$5053910111682$	$662062555387053$	$86730202577712721$	$11361656646684984330$	$1488377021704698764505$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which all are hyperelliptic):

• $y^2=31 x^6+7 x^5+52 x^4+47 x^3+25 x^2+11 x+128$
• $y^2=128 x^6+95 x^5+89 x^4+124 x^3+55 x^2+47 x+78$
• $y^2=76 x^6+6 x^5+108 x^4+34 x^3+73 x^2+19 x+119$
• $y^2=8 x^6+68 x^5+83 x^4+54 x^3+51 x^2+28 x+58$
• $y^2=127 x^6+127 x^5+79 x^4+19 x^3+112 x^2+118 x+40$
• $y^2=51 x^6+7 x^5+33 x^4+126 x^3+99 x^2+97 x+51$
• $y^2=118 x^6+45 x^5+124 x^4+57 x^3+86 x^2+68 x+66$
• $y^2=105 x^6+101 x^5+52 x^4+68 x^3+115 x^2+101 x+69$

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 4.0.3751992.1.

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_yi	$2$	(not in LMFDB)