Properties

Label 2.199.abx_bmh
Base Field $\F_{199}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 995 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.117818821654$, $\pm0.202443120192$
Angle rank:  $2$ (numerical)
Number field:  4.0.4943757.1
Galois group:  $D_{4}$
Jacobians:  16

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 30797 1552076409 62098831784483 2459465680592592477 97394122110296462549072 3856888374090007349193342489 152736585814262846196384801685871 6048521418836661273141296203633350933 239527496521795837948473540206582258665481 9485528389635274926547469145209710310984957184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39191 7879963 1568297539 312081026116 62103862448795 12358664525890561 2459374193488206835 489415464125017642849 97393677359601610254686

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.4943757.1.
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.bx_bmh$2$(not in LMFDB)