Properties

Label 2.191.aby_bmq
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 50 x + 1004 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0818372106519$, $\pm0.181493323579$
Angle rank:  $2$ (numerical)
Number field:  4.0.1583424.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27886 1313040196 48529985415334 1771210451423302864 64615221602584588672726 2357222203844399828792744356 85993801773629559054614242866046 3137139827612861276601533598385296384 114445997948299764604373829595858821168094 4175104451029753429223037275469998583644367076

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35990 6964822 1330873254 254195584202 48551239274726 9273284388935282 1771197287295783934 338298681569488144462 64615048177881495172550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.1583424.1.
All geometric endomorphisms are defined over $\F_{191}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.191.by_bmq$2$(not in LMFDB)