Properties

Label 2.199.acb_bqh
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:  $1 - 53 x + 1099 x^{2} - 10547 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0655121571235$, $\pm0.143829009609$
Angle rank:  $2$ (numerical)
Number field:  4.0.126125.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30101 1544211401 62058335623331 2459318867779118045 97393719107422634696496 3856887583988359986518479961 152736585155699418597894561542831 6048521421527014305278913876317772245 239527496537932164124653574620698446808801 9485528389684551496058859289805541603118454016

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 38991 7874823 1568203923 312079734772 62103849726531 12358664472602973 2459374194582124563 489415464157988252397 97393677360107562703006

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.126125.1.
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.cb_bqh$2$(not in LMFDB)