Abelian variety isogeny class 2.173.abt_bgt over $\F_{173}$

• Label: 2.173.abt_bgt
• Base field: $\F_{173}$
• 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:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 851 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.145147992759$, $\pm0.197931037552$
Angle rank:	$2$ (numerical)
Number field:	4.0.9725.1
Galois group:	$D_{4}$
Jacobians:	$11$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22951$	$886161061$	$26810859451819$	$802415155191647301$	$24014009244398486526736$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$129$	$29607$	$5178123$	$895807531$	$154965191694$	$26808771455943$	$4637914510420803$	$802359179578468723$	$138808137871611331209$	$24013807852348734248022$

Jacobians and polarizations

This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=103x^6+12x^5+18x^3+107x^2+119x+81$
• $y^2=60x^6+170x^5+2x^4+167x^3+3x^2+78x+111$
• $y^2=45x^6+94x^5+33x^4+31x^3+73x^2+114x+148$
• $y^2=3x^6+124x^5+28x^4+42x^3+72x^2+160x+51$
• $y^2=163x^6+37x^5+41x^4+154x^3+137x^2+30x+149$
• $y^2=2x^6+164x^5+132x^4+127x^3+67x^2+112x+80$
• $y^2=62x^6+106x^5+132x^4+154x^3+70x^2+131x+74$
• $y^2=2x^6+109x^5+102x^4+149x^3+137x^2+154x+51$
• $y^2=62x^6+165x^5+42x^4+163x^3+102x^2+68x+40$
• $y^2=25x^6+34x^5+26x^4+145x^3+48x^2+170x+43$
• $y^2=171x^6+97x^5+76x^4+92x^3+72x^2+158x+80$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The endomorphism algebra of this simple isogeny class is 4.0.9725.1.

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
2.173.bt_bgt	$2$	(not in LMFDB)