Properties

Label 2.199.abx_bmb
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:  $1 - 49 x + 989 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0696172273604$, $\pm0.224914406157$
Angle rank:  $2$ (numerical)
Number field:  4.0.1912493.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30791 1551589281 62091872695277 2459412645659510013 97393839515101513312016 3856887212648427231473902329 152736582019159833992376782973233 6048521409219206842882296465974141877 239527496505677954844829020809734841314643 9485528389636411722703534597748933979907712256

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39179 7879081 1568263723 312080120596 62103843747191 12358664218810207 2459374189577677699 489415464092084717173 97393677359613282430814

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.1912493.1.
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_bmb$2$(not in LMFDB)