# Properties

 Label 2.173.abt_bgl Base Field $\F_{173}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{173}$ Dimension: $2$ L-polynomial: $1 - 45 x + 843 x^{2} - 7785 x^{3} + 29929 x^{4}$ Frobenius angles: $\pm0.0769286473055$, $\pm0.234964715490$ Angle rank: $2$ (numerical) Number field: 4.0.17004349.1 Galois group: $D_{4}$ Jacobians: 17

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains the Jacobians of 17 curves, and hence is principally polarizable:

• $y^2=43x^6+107x^5+159x^4+47x^3+74x^2+69x+70$
• $y^2=84x^6+142x^5+101x^4+162x^3+134x^2+137x+73$
• $y^2=171x^6+23x^5+96x^4+32x^3+125x^2+14x+133$
• $y^2=6x^6+138x^5+163x^4+161x^3+82x^2+12x+60$
• $y^2=82x^6+94x^5+57x^4+154x^3+170x^2+30x+170$
• $y^2=105x^6+159x^5+18x^4+97x^3+11x^2+53x+87$
• $y^2=48x^6+25x^5+61x^4+2x^3+70x^2+138x+42$
• $y^2=101x^6+135x^5+11x^4+84x^3+15x^2+13x+63$
• $y^2=139x^6+31x^5+7x^4+18x^3+47x^2+90x+76$
• $y^2=127x^6+129x^5+45x^4+140x^3+137x^2+67x+67$
• $y^2=93x^6+4x^5+111x^4+35x^3+150x^2+89x+128$
• $y^2=52x^6+129x^5+12x^4+139x^3+154x^2+95x+153$
• $y^2=60x^6+65x^5+136x^4+x^3+4x^2+95x+82$
• $y^2=141x^6+138x^5+65x^4+28x^3+125x^2+42x+79$
• $y^2=90x^6+12x^5+46x^4+53x^3+155x^2+120x+117$
• $y^2=40x^6+3x^5+136x^4+22x^3+151x^2+162x+51$
• $y^2=79x^6+146x^5+94x^4+119x^3+25x^2+98x+11$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22943 885668629 26805259424531 802381386475467301 24013868660564699460368 718709299416601033414918261 21510249098252171299024335866027 643780250458724369482787787340984389 19267699139501291779292752896543037478519 576662967584304721262091998695377765194093824

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 129 29591 5177043 895769835 154964284494 26808754980647 4637914283058843 802359177446497459 138808137867701921289 24013807852701957868886

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The endomorphism algebra of this simple isogeny class is 4.0.17004349.1.
All geometric endomorphisms are defined over $\F_{173}$.

## 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_bgl $2$ (not in LMFDB)