Properties

Label 2.163.abr_bdy
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:  $1 - 43 x + 778 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0815159038334$, $\pm0.245687237918$
Angle rank:  $2$ (numerical)
Number field:  4.0.5575877.1
Galois group:  $D_{4}$
Jacobians:  48

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 48 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20296 698182400 18754624907488 498329377601408000 13239672427012164614296 351763895635251518279782400 9346014599521176454508749826872 248314265263904043542485602622976000 6597461723609103493431153208241146815712 175287960541296716944071312186371191860192000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26277 4330576 705937209 115063933911 18755369984694 3057125195108245 498311413563929841 81224760531726545968 13239635967179480706757

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.5575877.1.
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.br_bdy$2$(not in LMFDB)