# Properties

 Label 2.163.abv_bhr 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: $1 - 47 x + 875 x^{2} - 7661 x^{3} + 26569 x^{4}$ Frobenius angles: $\pm0.0428964655115$, $\pm0.176765590259$ Angle rank: $2$ (numerical) Number field: 4.0.40053.1 Galois group: $D_{4}$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=43x^6+124x^5+17x^4+68x^3+6x^2+143x+92$
• $y^2=100x^6+29x^5+156x^4+98x^3+68x^2+158x+97$
• $y^2=127x^6+92x^5+60x^4+156x^3+99x^2+20x+13$
• $y^2=124x^6+26x^5+55x^4+3x^3+98x^2+12x+51$
• $y^2=73x^6+68x^5+9x^4+115x^3+135x^2+128x+146$
• $y^2=54x^6+41x^5+29x^4+48x^3+18x^2+90x+32$
• $y^2=11x^6+56x^5+139x^4+110x^3+123x^2+144x+60$
• $y^2=44x^5+15x^4+130x^3+91x^2+86x+89$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 19737 693814761 18740517929523 498301938808875981 13239647886122274397392 351763935347013921976933377 9346014790353919039236765904647 248314265494466119028624314701773973 6597461722856576465525022944935875402741 175287960536216044277910335954612167420598016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 117 26111 4327317 705898339 115063720632 18755372102051 3057125257530531 498311414026616563 81224760522461796855 13239635966795733549446

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The endomorphism algebra of this simple isogeny class is 4.0.40053.1.
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.bv_bhr $2$ (not in LMFDB)