Properties

Label 2.163.abs_bfc
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:  $1 - 44 x + 808 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.130626345571$, $\pm0.201519655325$
Angle rank:  $2$ (numerical)
Number field:  4.0.1515776.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20162 697484228 18755185824626 498344828109050384 13239750128519234222082 351764143026800018839261700 9346015160053027651404613747058 248314266093439872473225114321567744 6597461723808347072647180337405088527234 175287960537859579439496109362752171464073028

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26250 4330704 705959094 115064609200 18755383175130 3057125378460840 498311415228623454 81224760534179536632 13239635966919871038250

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.1515776.1.
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.bs_bfc$2$(not in LMFDB)