# Properties

 Label 2.163.abv_bhs 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: $( 1 - 25 x + 163 x^{2} )( 1 - 22 x + 163 x^{2} )$ Frobenius angles: $\pm0.0652307277549$, $\pm0.169471200781$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=140x^6+162x^5+12x^4+133x^3+4x^2+117x+36$
• $y^2=161x^6+10x^5+97x^4+13x^3+95x^2+136x+25$
• $y^2=19x^6+61x^5+118x^4+146x^3+114x^2+61x+103$
• $y^2=22x^6+138x^5+158x^4+78x^3+129x^2+53x+82$
• $y^2=94x^6+78x^5+12x^4+5x^3+82x^2+97x+75$
• $y^2=70x^6+118x^5+28x^4+3x^3+69x^2+x+149$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 19738 693869652 18741129704584 498305704588028064 13239664678055109160198 351763995867747776897927616 9346014976339352433214833392566 248314265995952852723102043008476800 6597461724061444237479894470714188442536 175287960538814079750701002976819841202234452

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 117 26113 4327458 705903673 115063866567 18755375328898 3057125318367237 498311415032988721 81224760537295546614 13239635966991965188993

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.az $\times$ 1.163.aw 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.ad_aiq $2$ (not in LMFDB) 2.163.d_aiq $2$ (not in LMFDB) 2.163.bv_bhs $2$ (not in LMFDB) 2.163.ao_fu $3$ (not in LMFDB) 2.163.af_abw $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ad_aiq $2$ (not in LMFDB) 2.163.d_aiq $2$ (not in LMFDB) 2.163.bv_bhs $2$ (not in LMFDB) 2.163.ao_fu $3$ (not in LMFDB) 2.163.af_abw $3$ (not in LMFDB) 2.163.abn_bay $6$ (not in LMFDB) 2.163.abe_ti $6$ (not in LMFDB) 2.163.f_abw $6$ (not in LMFDB) 2.163.o_fu $6$ (not in LMFDB) 2.163.be_ti $6$ (not in LMFDB) 2.163.bn_bay $6$ (not in LMFDB)