Properties

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

Learn more about

Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 988 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0607284856894$, $\pm0.227683861456$
Angle rank:  $2$ (numerical)
Number field:  4.0.658952.3
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30790 1551508100 62090712867880 2459403784575380000 97393791880706733916450 3856887012264845295942190400 152736581326435842611007332655970 6048521407202243018115631099584080000 239527496500644427978817492093026350748360 9485528389625265805857775369315684701523702500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39177 7878934 1568258073 312079967961 62103840520602 12358664162758519 2459374188757565073 489415464081799944346 97393677359498840537377

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.658952.3.
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_bma$2$(not in LMFDB)