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

• Label: 2.139.abq_bbm
• 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:	$1 - 42 x + 714 x^{2} - 5838 x^{3} + 19321 x^{4}$
Frobenius angles:	$\pm0.0544053773055$, $\pm0.207067484893$
Angle rank:	$2$ (numerical)
Number field:	4.0.82000.1
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14156$	$366866896$	$7208152259996$	$139354860035226880$	$2692460178339168050396$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$98$	$18986$	$2683982$	$373304238$	$51888998378$	$7212550514906$	$1002544355282582$	$139353666708295198$	$19370159734131297938$	$2692452204110027159306$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=66x^6+105x^5+113x^4+91x^3+14x^2+12x+5$
• $y^2=100x^6+85x^5+37x^4+129x^3+15x^2+39x+85$
• $y^2=53x^6+30x^5+134x^4+52x^3+60x^2+88x+33$
• $y^2=92x^6+20x^5+71x^4+80x^3+35x^2+119x+104$
• $y^2=87x^6+93x^5+82x^4+112x^3+134x^2+8x+15$
• $y^2=34x^6+3x^5+8x^4+75x^3+136x^2+39x+41$
• $y^2=39x^6+133x^5+44x^4+98x^3+39x^2+62x+67$
• $y^2=92x^6+73x^5+23x^4+106x^3+74x^2+9x+12$
• $y^2=59x^6+85x^5+110x^4+109x^3+76x^2+68x+36$
• $y^2=27x^6+96x^5+99x^4+129x^3+21x^2+40x+133$
• $y^2=106x^6+53x^5+117x^4+4x^3+116x^2+32x+4$
• $y^2=48x^6+137x^5+21x^4+104x^3+28x^2+129x+69$
• $y^2=31x^6+95x^5+86x^4+7x^3+75x^2+33x+7$
• $y^2=64x^6+83x^5+x^4+12x^3+82x^2+62x+100$
• $y^2=4x^6+87x^5+27x^4+103x^3+98x^2+46x+27$
• $y^2=23x^6+51x^5+136x^4+20x^3+2x^2+53x+9$
• $y^2=58x^6+94x^5+76x^4+86x^3+99x^2+87x+3$
• $y^2=21x^6+56x^5+37x^4+71x^3+128x^2+39x+60$
• $y^2=64x^6+15x^5+81x^4+70x^3+21x^2+42x+60$
• $y^2=18x^6+52x^5+51x^4+116x^3+22x^2+48x+105$
• $y^2=61x^6+65x^5+30x^4+21x^3+30x^2+112x+12$
• $y^2=27x^6+87x^5+11x^4+41x^3+40x^2+132x+41$
• $y^2=86x^6+53x^5+34x^4+12x^3+131x^2+119x+3$
• $y^2=41x^6+130x^5+85x^4+116x^3+60x^2+107x+43$

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 4.0.82000.1.

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.bq_bbm	$2$	(not in LMFDB)