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

• Label: 2.131.abm_xl
• 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:	$1 - 38 x + 609 x^{2} - 4978 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0363854654428$, $\pm0.267764403510$
Angle rank:	$2$ (numerical)
Number field:	4.0.6224960.3
Galois group:	$D_{4}$
Jacobians:	$6$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12755$	$290648185$	$5053056462980$	$86730990520032665$	$1488371625323973323875$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$16936$	$2247712$	$294502596$	$38579349774$	$5053908187198$	$662062538549674$	$86730202578325956$	$11361656649078891952$	$1488377021740471775976$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=32x^6+19x^5+73x^4+37x^3+73x^2+95x+54$
• $y^2=55x^6+74x^5+114x^4+45x^3+93x^2+102x+81$
• $y^2=69x^6+x^5+95x^4+6x^3+87x^2+119x+94$
• $y^2=83x^6+74x^5+59x^4+83x^3+58x^2+86x+72$
• $y^2=10x^6+91x^5+80x^4+70x^3+90x^2+123x+59$
• $y^2=55x^6+47x^5+125x^4+21x^3+27x^2+94x+51$

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 4.0.6224960.3.

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.bm_xl	$2$	(not in LMFDB)