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

• Label: 2.131.abm_xs
• 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:	$1 - 38 x + 616 x^{2} - 4978 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.105476860213$, $\pm0.246682138343$
Angle rank:	$2$ (numerical)
Number field:	4.0.11154752.1
Galois group:	$D_{4}$
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12762$	$290897028$	$5054853985938$	$86737847812116048$	$1488389584149206230482$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$16950$	$2248510$	$294525878$	$38579815274$	$5053915247958$	$662062623293018$	$86730203401561054$	$11361656655903401518$	$1488377021799607745190$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=26x^6+38x^5+53x^4+81x^3+113x^2+63x+17$
• $y^2=71x^6+125x^5+80x^4+99x^3+32x^2+21x+51$
• $y^2=29x^6+123x^5+105x^4+76x^3+93x^2+2x+42$
• $y^2=97x^6+27x^5+24x^4+91x^3+76x^2+35x+59$
• $y^2=9x^6+42x^5+19x^4+19x^3+59x^2+49x+17$
• $y^2=30x^6+116x^5+44x^4+94x^3+91x^2+36x+17$
• $y^2=14x^6+109x^5+91x^4+100x^3+80x^2+120x+6$
• $y^2=106x^6+120x^5+4x^4+71x^3+120x^2+19x+106$
• $y^2=100x^6+71x^5+110x^4+115x^3+16x^2+32x+57$
• $y^2=19x^6+46x^5+16x^4+49x^3+81x^2+78x+73$
• $y^2=99x^6+56x^5+96x^4+87x^3+38x^2+99x+22$
• $y^2=77x^6+19x^5+83x^4+74x^3+10x^2+74x+70$
• $y^2=52x^6+94x^5+78x^4+49x^3+81x^2+95x+20$
• $y^2=42x^6+33x^5+18x^4+98x^3+50x^2+65x+116$
• $y^2=128x^6+65x^5+96x^4+85x^3+105x^2+x+29$
• $y^2=78x^6+28x^5+21x^4+25x^3+121x^2+127x+72$
• $y^2=29x^6+40x^5+78x^4+60x^3+14x^2+92x+81$
• $y^2=55x^6+39x^5+27x^4+14x^3+25x^2+128x+32$
• $y^2=112x^6+102x^5+22x^4+125x^3+12x^2+109x+125$
• $y^2=124x^6+46x^5+111x^4+83x^3+44x^2+52x+19$
• $y^2=45x^6+94x^5+76x^4+96x^3+55x^2+92x+123$
• $y^2=70x^6+47x^5+31x^4+96x^3+106x^2+67x+14$
• $y^2=82x^6+82x^5+18x^4+5x^3+76x^2+71x+32$
• $y^2=65x^6+91x^5+77x^4+47x^3+11x^2+16x+71$
• $y^2=79x^6+80x^5+90x^4+41x^3+34x^2+2x+23$
• $y^2=65x^6+40x^5+98x^4+51x^3+48x^2+105x+61$
• $y^2=76x^6+109x^5+24x^4+41x^3+103x^2+3x+121$
• $y^2=69x^6+61x^5+29x^4+96x^3+7x^2+14x+56$

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 4.0.11154752.1.

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.bm_xs	$2$	(not in LMFDB)