# Properties

 Label 2.163.abr_bec 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: $( 1 - 24 x + 163 x^{2} )( 1 - 19 x + 163 x^{2} )$ Frobenius angles: $\pm0.110906256499$, $\pm0.232879815243$ Angle rank: $2$ (numerical) Jacobians: 32

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 32 curves, and hence is principally polarizable:

• $y^2=121x^6+38x^5+155x^4+30x^3+136x^2+48x+143$
• $y^2=148x^6+76x^5+31x^4+113x^3+52x^2+158x+23$
• $y^2=16x^6+113x^5+89x^4+125x^3+58x^2+92x+101$
• $y^2=158x^6+112x^5+10x^4+110x^3+21x^2+55x+80$
• $y^2=114x^6+80x^5+18x^4+149x^3+128x^2+19x+133$
• $y^2=130x^6+3x^5+131x^4+26x^3+148x^2+121x+32$
• $y^2=61x^6+158x^5+2x^4+57x^3+37x^2+155x+107$
• $y^2=87x^6+66x^5+51x^4+136x^3+101x^2+95x+144$
• $y^2=109x^6+118x^5+117x^4+82x^3+79x^2+11x+81$
• $y^2=30x^6+6x^5+47x^4+24x^3+72x^2+89x+153$
• $y^2=137x^6+12x^5+45x^4+70x^3+34x^2+82x+73$
• $y^2=90x^6+44x^5+140x^4+88x^3+114x^2+24x+155$
• $y^2=124x^6+95x^5+39x^4+75x^3+153x^2+101x+119$
• $y^2=144x^6+128x^5+97x^4+59x^3+25x^2+148x+141$
• $y^2=150x^5+15x^4+81x^3+39x^2+49x+10$
• $y^2=131x^6+137x^5+114x^4+134x^3+24x^2+60x+73$
• $y^2=121x^6+79x^5+51x^4+53x^3+120x^2+107x+75$
• $y^2=18x^6+128x^5+55x^4+65x^3+63x^2+7x+80$
• $y^2=53x^6+132x^5+105x^4+59x^3+70x^2+43x+50$
• $y^2=23x^6+133x^5+90x^4+67x^3+18x^2+136x+52$
• and 12 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 20300 698401200 18756862938800 498341452495320000 13239717154708875582500 351764020207227936776428800 9346014864051384567920721737300 248314265660177081872110754708320000 6597461723847830045607080983504249242800 175287960540469755117365559799342320381630000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 121 26285 4331092 705954313 115064322631 18755376626630 3057125281637317 498311414359161553 81224760534665631916 13239635967117019636925

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.ay $\times$ 1.163.at 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.af_afa $2$ (not in LMFDB) 2.163.f_afa $2$ (not in LMFDB) 2.163.br_bec $2$ (not in LMFDB)