Properties

Label 2.199.abz_boh
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:  $1 - 51 x + 1047 x^{2} - 10149 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.107558551199$, $\pm0.167827717537$
Angle rank:  $2$ (numerical)
Number field:  4.0.440725.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30449 1548301201 62080947273431 2459410854718312429 97394023757570826483824 3856888427313984477047132161 152736587069523374445613064707979 6048521424722349970570832457141801909 239527496539719772014669099132655240321061 9485528389671163727796231401186976028997790976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 149 39095 7877693 1568262579 312080710964 62103863305811 12358664627459831 2459374195881372019 489415464161640788987 97393677359970102360350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.440725.1.
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.bz_boh$2$(not in LMFDB)