Properties

Label 2.163.abr_bdz
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:  $1 - 43 x + 779 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0890585227448$, $\pm0.242810877127$
Angle rank:  $2$ (numerical)
Number field:  4.0.21188013.2
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20297 698237097 18755184408299 498332400553350189 13239683683148189537072 351763927451355375738751473 9346014669855336971450256566063 248314265383145468920850580937731477 6597461723747528137340622457640005383653 175287960541347165620712221592120331290876672

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26279 4330705 705941491 115064031736 18755371681067 3057125218114879 498311413803220819 81224760533430763291 13239635967183291134534

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.21188013.2.
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.br_bdz$2$(not in LMFDB)