Properties

Label 2.199.aby_bnh
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:  $1 - 50 x + 1021 x^{2} - 9950 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.114292864932$, $\pm0.184902183990$
Angle rank:  $2$ (numerical)
Number field:  4.0.1507904.2
Galois group:  $D_{4}$
Jacobians:  15

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 15 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30623 1550228129 62090456785700 2459442447020867369 97394093908836770643903 3856888478039613492952490000 152736586642867908080321713574543 6048521422016991492879187817559596489 239527496529775289137496726063818816571300 9485528389645059306974297553112494885572573409

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 150 39144 7878900 1568282724 312080935750 62103864122598 12358664592937050 2459374194781352964 489415464141321686700 97393677359702072427304

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.1507904.2.
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.by_bnh$2$(not in LMFDB)