Properties

Label 2.163.abv_bhr
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon base change
2.163.bv_bhr$2$(not in LMFDB)