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

• Label: 2.157.abr_bdl
• 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:	$1 - 43 x + 765 x^{2} - 6751 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0408247231830$, $\pm0.242255315239$
Angle rank:	$2$ (numerical)
Number field:	4.0.76725.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18621$	$599763789$	$14971910056641$	$369148907776102821$	$9099059097050910510336$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$115$	$24331$	$3868819$	$607579315$	$95388984130$	$14976067398307$	$2351243161126303$	$369145192751482819$	$57955795529013965383$	$9099059900939207148886$

Jacobians and polarizations

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

• $y^2=85 x^6+24 x^5+66 x^4+11 x^3+62 x^2+41 x+127$
• $y^2=18 x^6+58 x^5+6 x^4+126 x^3+144 x^2+52 x+118$
• $y^2=135 x^6+108 x^5+63 x^4+67 x^3+89 x^2+123 x+127$
• $y^2=142 x^6+136 x^5+144 x^4+x^3+83 x^2+112 x+15$
• $y^2=103 x^6+104 x^5+137 x^4+111 x^3+133 x^2+85 x+87$
• $y^2=58 x^6+18 x^5+7 x^4+61 x^3+27 x^2+71 x+15$
• $y^2=24 x^6+107 x^5+93 x^4+3 x^3+20 x^2+55 x+124$
• $y^2=111 x^6+103 x^5+31 x^4+88 x^3+37 x^2+146 x+114$
• $y^2=132 x^6+x^5+79 x^4+16 x^3+112 x^2+78 x+114$
• $y^2=136 x^6+61 x^5+26 x^4+35 x^3+138 x^2+30 x+133$
• $y^2=119 x^6+28 x^5+11 x^4+4 x^3+58 x^2+135 x+78$
• $y^2=63 x^6+2 x^5+75 x^4+119 x^3+4 x^2+88 x+104$
• $y^2=146 x^6+127 x^5+76 x^4+18 x^3+44 x^2+108 x+102$
• $y^2=38 x^6+88 x^5+54 x^4+138 x^3+139 x^2+108 x+119$
• $y^2=17 x^6+128 x^5+129 x^4+97 x^3+10 x^2+50 x+125$
• $y^2=98 x^6+60 x^5+136 x^4+81 x^3+22 x^2+83 x+150$

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 4.0.76725.1.

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.br_bdl	$2$	(not in LMFDB)