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

• Label: 2.139.abn_ys
• 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:	$1 - 39 x + 642 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:	$\pm0.0204242639044$, $\pm0.272236041847$
Angle rank:	$2$ (numerical)
Number field:	4.0.764725.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14504$	$368749696$	$7211289070496$	$139353579590869504$	$2692439756654449565624$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$101$	$19085$	$2685152$	$373300809$	$51888604811$	$7212542249126$	$1002544250819849$	$139353665928286609$	$19370159733675520928$	$2692452204180544474925$

Jacobians and polarizations

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

• $y^2=16x^6+122x^5+127x^4+29x^3+54x^2+96x+55$
• $y^2=69x^6+40x^5+95x^4+13x^3+74x^2+49x+66$
• $y^2=16x^6+25x^5+103x^4+99x^3+36x^2+95x+12$
• $y^2=114x^6+127x^5+112x^4+99x^3+109x^2+78x+74$
• $y^2=74x^6+28x^5+20x^4+99x^3+24x^2+76x+40$
• $y^2=101x^6+46x^5+64x^4+72x^3+94x^2+76x+67$
• $y^2=74x^5+27x^4+6x^3+114x^2+125x+11$
• $y^2=29x^6+121x^5+131x^4+82x^3+131x^2+x+41$
• $y^2=46x^6+97x^5+60x^4+70x^3+66x^2+83x+78$
• $y^2=130x^6+36x^5+19x^4+67x^3+9x^2+87x+62$
• $y^2=30x^6+44x^5+83x^4+23x^3+116x^2+29x+92$
• $y^2=136x^6+82x^5+21x^4+104x^3+116x^2+2x+41$
• $y^2=77x^6+111x^5+23x^4+66x^3+62x^2+53x+95$
• $y^2=111x^6+132x^5+66x^4+33x^3+26x^2+8x+132$
• $y^2=100x^6+126x^5+90x^4+87x^3+92x^2+69x+88$
• $y^2=61x^6+80x^5+17x^4+62x^3+39x^2+51x+66$

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 4.0.764725.2.

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.bn_ys	$2$	(not in LMFDB)