Abelian variety isogeny class 2.139.abo_baa over $\F_{139}$

• Label: 2.139.abo_baa
• Base field: $\F_{139}$
• 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:	$\F_{139}$
Dimension:	$2$
L-polynomial:	$1 - 40 x + 676 x^{2} - 5560 x^{3} + 19321 x^{4}$
Frobenius angles:	$\pm0.137483446999$, $\pm0.211006567308$
Angle rank:	$2$ (numerical)
Number field:	4.0.1313024.1
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14398$	$368560004$	$7213735273150$	$139368649481534864$	$2692488620005476820078$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$100$	$19074$	$2686060$	$373341174$	$51889546500$	$7212557593938$	$1002544435876300$	$139353667505973534$	$19370159740527144580$	$2692452204139069079554$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=76x^6+60x^5+28x^4+122x^3+98x^2+15x+22$
• $y^2=97x^6+39x^5+31x^4+46x^3+89x^2+85x+1$
• $y^2=133x^6+34x^5+46x^4+56x^3+90x^2+109x+102$
• $y^2=19x^6+99x^5+32x^4+40x^3+35x^2+114x+122$
• $y^2=x^6+94x^5+36x^4+133x^3+53x^2+124x+88$
• $y^2=x^6+37x^5+74x^4+60x^3+17x^2+122x+21$
• $y^2=58x^6+56x^5+133x^4+104x^3+101x^2+96x$
• $y^2=72x^6+63x^5+91x^4+40x^3+101x^2+62x+122$
• $y^2=32x^6+75x^5+54x^4+10x^3+46x^2+121x+51$
• $y^2=32x^6+52x^5+115x^4+39x^3+32x^2+81x+10$
• $y^2=88x^6+95x^5+94x^4+28x^3+109x^2+48x+31$
• $y^2=23x^6+35x^5+109x^4+115x^3+51x^2+12x+55$
• $y^2=56x^6+77x^5+30x^4+65x^3+102x^2+109x+4$
• $y^2=101x^6+134x^5+75x^4+25x^3+135x^2+110x+132$
• $y^2=123x^6+78x^5+108x^4+45x^3+62x^2+61x+52$
• $y^2=62x^6+99x^5+21x^4+52x^3+138x^2+118x+74$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{139}$.

Endomorphism algebra over $\F_{139}$

The endomorphism algebra of this simple isogeny class is 4.0.1313024.1.

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
2.139.bo_baa	$2$	(not in LMFDB)