# Properties

 Label 2.163.abs_beu 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: $1 - 44 x + 800 x^{2} - 7172 x^{3} + 26569 x^{4}$ Frobenius angles: $\pm0.0544015131199$, $\pm0.235892031164$ Angle rank: $2$ (numerical) Number field: 4.0.8966400.1 Galois group: $D_{4}$ Jacobians: 12

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 12 curves, and hence is principally polarizable:

• $y^2=25x^6+132x^5+29x^4+19x^3+46x^2+83x+95$
• $y^2=68x^6+80x^5+75x^4+54x^3+148x^2+7x+43$
• $y^2=114x^6+45x^5+x^4+142x^3+78x^2+32x+54$
• $y^2=140x^6+92x^5+36x^4+116x^3+58x^2+93x+70$
• $y^2=92x^6+72x^5+44x^4+41x^3+112x^2+145x+31$
• $y^2=109x^6+18x^4+110x^3+36x^2+133x+158$
• $y^2=157x^6+98x^5+26x^4+28x^3+67x^2+156x+60$
• $y^2=123x^6+82x^5+160x^4+12x^3+98x^2+158x+24$
• $y^2=141x^6+35x^5+160x^4+58x^3+20x^2+28x+161$
• $y^2=113x^6+125x^5+3x^4+89x^3+24x^2+111x+97$
• $y^2=126x^6+112x^5+155x^4+126x^3+29x^2+x+147$
• $y^2=66x^6+39x^5+150x^4+122x^3+55x^2+30x+86$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 20154 697046244 18750605251914 498319254842977296 13239650694675594215514 351763846434730614714341796 9346014462173258990602600942314 248314264837753790602568041152528384 6597461722378049233674707942468928393786 175287960538274245172496395495092430197553124

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 120 26234 4329648 705922870 115063745040 18755367361418 3057125150181096 498311412708741214 81224760516570400824 13239635966951191063514

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The endomorphism algebra of this simple isogeny class is 4.0.8966400.1.
All geometric endomorphisms are defined over $\F_{163}$.

## 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 2.163.bs_beu $2$ (not in LMFDB)