Properties

Label 2.199.aby_bnh
Base field $\F_{199}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
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, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $30623$ $1550228129$ $62090456785700$ $2459442447020867369$ $97394093908836770643903$

Point counts of the curve

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

Jacobians and polarizations

This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{199}$.

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.1507904.2.

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)