Abelian variety isogeny class 2.157.abq_bcq over $\F_{157}$

• Label: 2.157.abq_bcq
• Base field: $\F_{157}$
• 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:	$\F_{157}$
Dimension:	$2$
L-polynomial:	$1 - 42 x + 744 x^{2} - 6594 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0777208645174$, $\pm0.250658032141$
Angle rank:	$2$ (numerical)
Number field:	4.0.22403392.1
Galois group:	$D_{4}$
Jacobians:	$32$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18758$	$600818740$	$14975583776102$	$369158378766619600$	$9099080930405157882278$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$116$	$24374$	$3869768$	$607594902$	$95389213016$	$14976070918166$	$2351243221354388$	$369145193811995998$	$57955795546387234916$	$9099059901189269933414$

Jacobians and polarizations

This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=115x^6+134x^5+36x^4+115x^3+27x^2+44x+16$
• $y^2=135x^6+91x^5+4x^4+19x^3+45x^2+135x$
• $y^2=25x^6+21x^5+115x^4+154x^3+58x^2+140x+60$
• $y^2=2x^6+130x^5+31x^4+80x^3+95x^2+54x+91$
• $y^2=121x^6+141x^5+63x^4+121x^3+16x^2+154x+74$
• $y^2=66x^6+35x^5+8x^4+34x^3+155x^2+80x+63$
• $y^2=142x^6+136x^5+75x^4+112x^3+24x^2+83x+29$
• $y^2=92x^6+105x^5+130x^4+93x^3+131x^2+116x+88$
• $y^2=82x^6+114x^5+132x^4+28x^3+135x^2+37x+15$
• $y^2=133x^6+69x^5+95x^4+84x^3+99x^2+78x+136$
• $y^2=93x^6+114x^5+123x^4+106x^3+34x^2+13x+117$
• $y^2=66x^6+104x^5+26x^4+17x^3+87x^2+153x+72$
• $y^2=119x^6+90x^5+30x^4+130x^3+50x^2+110x+142$
• $y^2=126x^6+64x^5+131x^4+22x^3+60x^2+150x+35$
• $y^2=118x^6+48x^5+137x^4+15x^3+93x^2+64x+99$
• $y^2=61x^6+5x^5+126x^4+151x^3+66x^2+112x+61$
• $y^2=28x^6+149x^5+133x^4+33x^3+110x^2+26x+60$
• $y^2=88x^6+34x^5+26x^4+44x^3+7x+8$
• $y^2=25x^6+38x^5+55x^4+133x^3+19x^2+90x+1$
• $y^2=134x^6+31x^5+102x^4+147x^3+132x^2+76x+44$
• and

• $y^2=92x^6+34x^5+51x^4+143x^3+55x^2+66x+77$
• $y^2=151x^6+42x^5+136x^4+53x^3+76x^2+66x+78$
• $y^2=98x^6+29x^5+87x^4+62x^3+121x^2+111x+146$
• $y^2=125x^6+17x^5+6x^4+75x^3+60x^2+39x+24$
• $y^2=61x^6+21x^5+145x^4+108x^3+74x^2+155x+95$
• $y^2=29x^6+92x^5+152x^4+123x^3+92x^2+115x+152$
• $y^2=9x^6+145x^5+115x^4+44x^3+60x^2+44x+63$
• $y^2=63x^6+18x^5+23x^4+43x^3+147x^2+21x+77$
• $y^2=156x^6+22x^5+17x^4+118x^3+108x^2+67x+128$
• $y^2=89x^6+141x^5+70x^4+68x^3+145x^2+87x+6$
• $y^2=95x^6+116x^5+4x^4+19x^3+90x^2+67x+11$
• $y^2=32x^6+20x^5+60x^4+106x^3+102x^2+56x+136$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The endomorphism algebra of this simple isogeny class is 4.0.22403392.1.

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
2.157.bq_bcq	$2$	(not in LMFDB)