# Properties

 Label 2.163.abw_bis Base Field $\F_{163}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{163}$ Dimension: $2$ L-polynomial: $( 1 - 24 x + 163 x^{2} )^{2}$ Frobenius angles: $\pm0.110906256499$, $\pm0.110906256499$ Angle rank: $1$ (numerical) Jacobians: 14

This isogeny class is not 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 14 curves, and hence is principally polarizable:

• $y^2=16x^6+99x^4+99x^2+16$
• $y^2=6x^6+140x^5+121x^4+124x^3+121x^2+140x+6$
• $y^2=58x^6+101x^5+36x^4+91x^3+74x^2+129x+20$
• $y^2=52x^6+150x^5+51x^4+51x^3+54x^2+83x+32$
• $y^2=112x^6+89x^5+42x^4+161x^3+128x^2+121x+162$
• $y^2=118x^6+70x^4+70x^2+118$
• $y^2=52x^6+102x^5+37x^4+145x^3+79x^2+145x+20$
• $y^2=34x^6+23x^5+139x^4+104x^3+139x^2+23x+34$
• $y^2=52x^6+26x^5+95x^4+81x^3+95x^2+26x+52$
• $y^2=118x^6+97x^5+20x^4+x^3+129x^2+132x+10$
• $y^2=113x^6+103x^4+103x^2+113$
• $y^2=109x^6+70x^5+123x^4+73x^3+117x^2+7x+103$
• $y^2=107x^6+16x^5+115x^4+130x^3+115x^2+16x+107$
• $y^2=121x^6+6x^5+128x^4+124x^3+19x^2+71x+99$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 19600 692742400 18737297395600 498298198325760000 13239662582857049290000 351764049369583674937657600 9346015256458778963967678691600 248314266959430677226754206965760000 6597461726709980907866463679260940531600 175287960544900297010000085190495207353760000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 116 26070 4326572 705893038 115063848356 18755378181510 3057125409995612 498311416966474078 81224760569903050196 13239635967451661911350

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-19})$$$)$
All geometric endomorphisms are defined over $\F_{163}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.a_ajq $2$ (not in LMFDB) 2.163.bw_bis $2$ (not in LMFDB) 2.163.y_px $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.a_ajq $2$ (not in LMFDB) 2.163.bw_bis $2$ (not in LMFDB) 2.163.y_px $3$ (not in LMFDB) 2.163.a_jq $4$ (not in LMFDB) 2.163.ay_px $6$ (not in LMFDB)