Properties

Label 2.199.abx_blz
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:  $1 - 49 x + 987 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0508592358596$, $\pm0.230295663413$
Angle rank:  $2$ (numerical)
Number field:  4.0.175725.1
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30789 1551426921 62089553046411 2459394917225867709 97393744093398804550224 3856886809933565834425432521 152736580616442077435075994492999 6048521405065777739360053716673194069 239527496494925615253822646861767061476081 9485528389610742661143011758656632504711122176

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39175 7878787 1568252419 312079814836 62103837262651 12358664105309449 2459374187888862259 489415464070114958593 97393677359349722595550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.175725.1.
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_blz$2$(not in LMFDB)