# Properties

 Label 2.163.abu_bgt 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: $( 1 - 25 x + 163 x^{2} )( 1 - 21 x + 163 x^{2} )$ Frobenius angles: $\pm0.0652307277549$, $\pm0.192621479609$ Angle rank: $2$ (numerical) Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=120x^6+98x^5+150x^4+7x^3+150x^2+98x+120$
• $y^2=123x^6+88x^5+143x^4+11x^3+129x^2+81x+12$
• $y^2=112x^6+13x^5+143x^4+124x^3+87x^2+142x+118$
• $y^2=106x^6+11x^5+107x^4+82x^3+107x^2+11x+106$
• $y^2=17x^6+121x^5+25x^4+80x^3+127x^2+144x+47$
• $y^2=44x^6+3x^5+97x^4+37x^3+51x^2+153x+105$
• $y^2=126x^6+36x^5+117x^4+17x^3+117x^2+36x+126$
• $y^2=139x^6+90x^5+158x^4+134x^3+158x^2+90x+139$
• $y^2=122x^6+82x^5+52x^4+3x^3+52x^2+82x+122$
• $y^2=53x^6+136x^5+83x^4+22x^3+83x^2+136x+53$
• $y^2=144x^6+114x^5+60x^4+5x^3+60x^2+114x+144$
• $y^2=117x^6+117x^5+139x^4+85x^3+44x^2+150x+138$
• $y^2=42x^6+69x^5+13x^4+110x^3+13x^2+69x+42$
• $y^2=37x^6+18x^5+52x^4+134x^3+52x^2+18x+37$
• $y^2=152x^6+16x^5+123x^4+111x^3+148x^2+129x+74$
• $y^2=53x^6+121x^5+145x^4+74x^3+81x^2+51x+105$
• $y^2=27x^6+53x^5+150x^4+8x^3+29x^2+65x+136$
• $y^2=120x^6+151x^5+130x^4+8x^3+143x^2+78x+92$
• $y^2=68x^6+128x^5+116x^4+160x^3+124x^2+16x+137$
• $y^2=53x^6+8x^5+138x^4+122x^3+138x^2+8x+53$
• $y^2=155x^6+79x^5+116x^4+10x^3+116x^2+79x+155$
• $y^2=32x^6+90x^5+46x^4+73x^3+46x^2+90x+32$
• $y^2=8x^6+100x^5+111x^4+55x^3+63x^2+87x+128$
• $y^2=103x^6+119x^5+59x^4+109x^3+49x^2+144x+115$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 19877 694999305 18745015663088 498313990860510825 13239672959273330652797 351763977038034823876373760 9346014849578984138620167745493 248314265597665847584185700429535625 6597461723196874004506798373211405278192 175287960537598439853291467606869972049864025

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 118 26156 4328356 705915412 115063938538 18755374324934 3057125276903326 498311414233715428 81224760526651375708 13239635966900146962236

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.az $\times$ 1.163.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ae_ahr $2$ (not in LMFDB) 2.163.e_ahr $2$ (not in LMFDB) 2.163.bu_bgt $2$ (not in LMFDB) 2.163.an_gc $3$ (not in LMFDB) 2.163.ae_abf $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ae_ahr $2$ (not in LMFDB) 2.163.e_ahr $2$ (not in LMFDB) 2.163.bu_bgt $2$ (not in LMFDB) 2.163.an_gc $3$ (not in LMFDB) 2.163.ae_abf $3$ (not in LMFDB) 2.163.abm_bah $6$ (not in LMFDB) 2.163.abd_ta $6$ (not in LMFDB) 2.163.e_abf $6$ (not in LMFDB) 2.163.n_gc $6$ (not in LMFDB) 2.163.bd_ta $6$ (not in LMFDB) 2.163.bm_bah $6$ (not in LMFDB)