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

• Label: 2.131.abn_yh
• 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:	$1 - 39 x + 631 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0180869175517$, $\pm0.250795763867$
Angle rank:	$2$ (numerical)
Number field:	4.0.11125.1
Galois group:	$D_{4}$
Jacobians:	$10$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12645$	$290088945$	$5052070139895$	$86730462364791645$	$1488373055579493450000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16903$	$2247273$	$294500803$	$38579386848$	$5053908839443$	$662062537437303$	$86730202350938323$	$11361656643902439903$	$1488377021668510504198$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=4x^6+7x^5+19x^4+123x^3+x^2+36x+87$
• $y^2=122x^6+92x^5+12x^4+87x^3+42x^2+104x+73$
• $y^2=69x^6+17x^5+32x^4+72x^3+120x^2+72x+2$
• $y^2=10x^6+82x^5+109x^4+73x^3+93x^2+45x+66$
• $y^2=34x^6+16x^5+63x^4+25x^3+54x^2+115x+103$
• $y^2=102x^6+47x^5+124x^4+49x^3+69x^2+105x+92$
• $y^2=60x^6+85x^5+79x^4+122x^3+70x^2+114x+114$
• $y^2=82x^6+78x^5+70x^4+108x^3+60x^2+57x+90$
• $y^2=32x^6+67x^5+108x^4+46x^3+79x^2+54x+96$
• $y^2=111x^6+69x^5+64x^4+117x^3+14x^2+100x+84$

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 4.0.11125.1.

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_yh	$2$	(not in LMFDB)