# Properties

 Label 2.163.abs_bfd 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: $( 1 - 23 x + 163 x^{2} )( 1 - 21 x + 163 x^{2} )$ Frobenius angles: $\pm0.143017980409$, $\pm0.192621479609$ Angle rank: $2$ (numerical) Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=66x^6+98x^5+55x^4+14x^3+115x^2+124x+148$
• $y^2=127x^6+144x^5+160x^4+162x^3+111x^2+69x+27$
• $y^2=57x^6+81x^5+75x^4+149x^3+86x^2+34x+113$
• $y^2=110x^6+21x^5+125x^4+106x^3+2x^2+131x+142$
• $y^2=13x^6+80x^5+129x^4+46x^3+149x^2+13x+123$
• $y^2=96x^6+142x^5+151x^4+153x^3+91x^2+59x+35$
• $y^2=3x^6+153x^5+86x^4+133x^3+80x^2+17x+18$
• $y^2=162x^6+113x^5+155x^4+26x^3+43x^2+160x+48$
• $y^2=70x^6+52x^5+9x^4+51x^3+49x^2+12x+159$
• $y^2=128x^6+18x^5+153x^4+16x^3+76x^2+3x+153$
• $y^2=89x^6+84x^5+51x^4+27x^3+x^2+151x+76$
• $y^2=95x^6+88x^5+106x^4+162x^3+149x^2+62x+93$
• $y^2=154x^6+140x^5+114x^4+27x^3+28x^2+69x+101$
• $y^2=70x^6+87x^5+140x^4+149x^3+144x^2+15x+63$
• $y^2=130x^6+73x^5+59x^4+95x^3+66x^2+8x+116$
• $y^2=85x^6+39x^5+113x^4+65x^3+4x^2+121x+65$
• $y^2=76x^6+35x^5+28x^4+44x^3+106x^2+65x+42$
• $y^2=8x^6+8x^5+109x^4+55x^3+68x^2+82x+102$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 20163 697538985 18755758417968 498348012083632425 13239762329938211361723 351764177975644244923157760 9346015233576500732290039838979 248314266182037699972042457393161225 6597461723708959919345362999040193928752 175287960536858539324477701783840826443706425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 120 26252 4330836 705963604 115064715240 18755385038534 3057125402510712 498311415406419556 81224760532955930028 13239635966844261699932

## Decomposition and endomorphism algebra

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