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

• Label: 2.157.abr_bdr
• 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:	$1 - 43 x + 771 x^{2} - 6751 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.101717076357$, $\pm0.221991051519$
Angle rank:	$2$ (numerical)
Number field:	4.0.7079373.1
Galois group:	$D_{4}$
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18627$	$600068805$	$14974910302527$	$369164672104683525$	$9099116931647620166352$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$115$	$24343$	$3869593$	$607605259$	$95389590430$	$14976078359191$	$2351243321107201$	$369145194660056371$	$57955795547488062091$	$9099059901082870732918$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=50x^6+130x^5+92x^4+80x^3+103x^2+44x+4$
• $y^2=93x^6+121x^5+73x^4+40x^3+55x^2+130x+32$
• $y^2=66x^6+116x^5+81x^4+2x^3+31x^2+53x+57$
• $y^2=104x^6+88x^5+43x^4+92x^3+55x^2+21x+57$
• $y^2=150x^6+141x^5+6x^4+61x^3+x^2+12x+26$
• $y^2=81x^6+134x^5+83x^4+25x^3+54x^2+83x+134$
• $y^2=149x^6+139x^5+130x^4+47x^3+2x^2+96x+6$
• $y^2=126x^6+135x^5+123x^4+118x^3+92x^2+94x+129$
• $y^2=132x^6+5x^5+40x^4+93x^3+82x^2+142x+121$
• $y^2=86x^6+21x^5+124x^4+36x^3+126x^2+131x+109$
• $y^2=84x^6+89x^5+153x^4+24x^3+107x^2+64x+73$
• $y^2=11x^6+119x^5+151x^4+66x^3+2x^2+83x+124$
• $y^2=134x^6+99x^5+41x^4+24x^3+134x^2+45x+57$
• $y^2=59x^6+22x^5+82x^4+146x^3+84x^2+53x+112$
• $y^2=98x^6+126x^5+40x^4+48x^3+79x^2+106x+48$
• $y^2=9x^6+75x^5+128x^4+54x^3+10x^2+26x+102$
• $y^2=131x^6+87x^5+89x^4+36x^3+16x^2+128x+88$
• $y^2=83x^6+126x^5+21x^4+74x^3+68x^2+104x+65$
• $y^2=71x^6+147x^5+146x^4+126x^3+13x^2+39x+125$
• $y^2=27x^6+97x^5+83x^4+4x^3+127x^2+76x+102$
• $y^2=54x^6+87x^5+71x^4+24x^3+110x^2+150x+104$
• $y^2=114x^6+127x^5+46x^4+79x^3+94x^2+29x+145$
• $y^2=142x^6+53x^5+53x^4+119x^3+19x^2+59x+9$
• $y^2=4x^6+61x^5+22x^4+56x^3+97x^2+45x+11$
• $y^2=4x^6+88x^5+52x^4+21x^3+87x^2+74x+38$
• $y^2=44x^6+103x^5+94x^4+156x^3+17x^2+5x+15$
• $y^2=16x^6+85x^5+43x^4+129x^3+104x^2+89x+120$
• $y^2=155x^6+39x^5+137x^4+116x^3+11x^2+118x+155$

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 4.0.7079373.1.

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_bdr	$2$	(not in LMFDB)