Properties

Label 2.199.abx_blx
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:  $1 - 49 x + 985 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:  $\pm0.0229683311136$, $\pm0.235127646112$
Angle rank:  $2$ (numerical)
Number field:  4.0.4193837.1
Galois group:  $D_{4}$
Jacobians:  7

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 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30787 1551264569 62087233421233 2459377163730601517 97393648060043324074672 3856886399424933154053317489 152736579144543489017842677797341 6048521400432541495428011514379268693 239527496481410100073852232030117525066551 9485528389571355695607293529241034752885603584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39171 7878493 1568241099 312079507116 62103830652615 12358663986210931 2459374186004953635 489415464042499331029 97393677358945312713886

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is 4.0.4193837.1.
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_blx$2$(not in LMFDB)