Properties

Label 2.199.aca_bpg
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:  $1 - 52 x + 1072 x^{2} - 10348 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0759470812814$, $\pm0.163199525114$
Angle rank:  $2$ (numerical)
Number field:  4.0.545024.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30274 1546214276 62069024885122 2459359746395334416 97393840761067648525474 3856887858022279786406442884 152736585515030250461136549302434 6048521421058804970950352584136474624 239527496532809355490184618063565954131842 9485528389664127202401972176748933997315100676

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 148 39042 7876180 1568229990 312080124588 62103854139042 12358664501678188 2459374194391747134 489415464147521054260 97393677359897854083202

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.545024.2.
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.ca_bpg$2$(not in LMFDB)