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

• Label: 2.131.abn_yk
• 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:	$1 - 39 x + 634 x^{2} - 5109 x^{3} + 17161 x^{4}$
Frobenius angles:	$\pm0.0678955370439$, $\pm0.241198846124$
Angle rank:	$2$ (numerical)
Number field:	4.0.1582317.1
Galois group:	$D_{4}$
Jacobians:	$44$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$12648$	$290195712$	$5052860872992$	$86733602700715008$	$1488381789826992270648$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$16909$	$2247624$	$294511465$	$38579613243$	$5053912596790$	$662062589196465$	$86730202973983633$	$11361656650950410040$	$1488377021751682543549$

Jacobians and polarizations

This isogeny class contains the Jacobians of 44 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=120x^6+119x^5+89x^4+23x^3+15x^2+108x+56$
• $y^2=3x^6+13x^5+120x^4+47x^3+62x^2+118x+117$
• $y^2=60x^6+23x^5+112x^4+125x^3+80x^2+69x+126$
• $y^2=3x^6+4x^5+54x^4+60x^3+86x^2+68x+93$
• $y^2=115x^6+72x^5+39x^4+84x^3+14x^2+59x+71$
• $y^2=77x^6+82x^5+30x^4+84x^3+84x^2+101x+3$
• $y^2=122x^6+4x^5+21x^4+30x^3+46x^2+75x+80$
• $y^2=111x^6+113x^5+13x^4+8x^3+20x^2+44x+99$
• $y^2=24x^6+27x^5+123x^4+68x^3+29x^2+22x+65$
• $y^2=23x^6+95x^5+82x^4+67x^3+124x^2+83x+93$
• $y^2=9x^6+119x^5+104x^4+46x^3+54x^2+22x+124$
• $y^2=88x^6+18x^5+63x^4+5x^3+120x^2+123x+91$
• $y^2=47x^5+17x^4+77x^3+8x^2+5x+7$
• $y^2=78x^6+91x^5+49x^4+130x^3+x^2+6x+40$
• $y^2=47x^6+55x^5+60x^4+6x^3+36x^2+60x+20$
• $y^2=27x^6+16x^5+125x^4+116x^3+39x^2+34x+127$
• $y^2=10x^6+103x^5+71x^4+28x^3+35x^2+99x+86$
• $y^2=102x^6+66x^5+45x^4+69x^3+22x^2+98x+48$
• $y^2=22x^6+66x^5+54x^4+20x^3+50x^2+80x+36$
• $y^2=42x^6+88x^5+125x^4+15x^3+36x^2+73x+52$
• and

• $y^2=104x^6+102x^5+116x^4+12x^3+89x^2+31x+112$
• $y^2=30x^6+106x^5+41x^4+57x^3+22x^2+27x+78$
• $y^2=93x^6+111x^5+69x^4+84x^3+93x^2+85x+116$
• $y^2=125x^6+25x^5+106x^4+17x^3+43x^2+15x+34$
• $y^2=98x^6+32x^5+28x^4+29x^3+26x^2+84x+61$
• $y^2=120x^6+44x^5+82x^4+64x^3+78x^2+55x+102$
• $y^2=14x^6+24x^5+20x^4+74x^3+53x^2+42x+126$
• $y^2=126x^6+21x^5+89x^4+53x^3+64x^2+25x+99$
• $y^2=101x^6+124x^5+71x^4+127x^3+10x^2+38x+90$
• $y^2=17x^6+72x^5+56x^4+130x^3+24x^2+110x+39$
• $y^2=48x^6+80x^5+38x^4+122x^3+103x^2+16x+78$
• $y^2=122x^6+33x^5+70x^4+106x^3+94x^2+99x+79$
• $y^2=31x^6+114x^5+99x^4+126x^3+57x^2+115x+120$
• $y^2=84x^6+98x^5+19x^4+106x^3+26x^2+76x+69$
• $y^2=97x^6+56x^5+70x^4+46x^3+121x^2+36x+18$
• $y^2=48x^6+90x^5+43x^4+91x^3+113x^2+67x+66$
• $y^2=48x^6+109x^5+77x^4+81x^3+28x^2+126x+63$
• $y^2=3x^6+94x^5+71x^4+129x^3+3x^2+26x+77$
• $y^2=93x^5+107x^4+6x^3+53x^2+40x+74$
• $y^2=30x^6+11x^5+129x^4+116x^3+29x^2+42x+60$
• $y^2=101x^6+2x^5+2x^4+7x^3+40x^2+32x+29$
• $y^2=130x^6+99x^5+116x^4+66x^3+129x^2+84x+17$
• $y^2=128x^6+86x^5+17x^4+121x^3+122x^2+85x+120$
• $y^2=48x^6+56x^5+29x^4+103x^3+114x^2+83x+16$

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 4.0.1582317.1.

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_yk	$2$	(not in LMFDB)