Properties

Label 2.199.abw_bkx
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 959 x^{2} - 9552 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0495023584196$, $\pm0.247161933256$
Angle rank:  $2$ (numerical)
Number field:  4.0.26874000.1
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
$A(\F_{q^r})$ 30961 1553034721 62094758540836 2459397377579792265 97393686182777253789121 3856886486715102893545985296 152736579672793790024004455202961 6048521403908141771560523558829373065 239527496498707057388838990936338875201636 9485528389638011423539349848860803809089728641

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 152 39216 7879448 1568253988 312079629272 62103832058166 12358664028954248 2459374187418158788 489415464077841404552 97393677359629707530256

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.26874000.1.
All geometric endomorphisms are defined over $\F_{199}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.bw_bkx$2$(not in LMFDB)