Properties

Label 2.191.abv_bjn
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:  $1 - 47 x + 923 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0761135416416$, $\pm0.240053756085$
Angle rank:  $2$ (numerical)
Number field:  4.0.383725.4
Galois group:  $D_{4}$
Jacobians:  27

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 27 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28381 1317701449 48546969442891 1771237659671215069 64615161484954782005776 2357221606891391113335535225 85993799414104077320564592342871 3137139821715607350942217033867061589 114445997940882519098685812714130771438121 4175104451043488220511904288144368641526653184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36119 6967261 1330893699 254195347700 48551226979403 9273284134491935 1771197283966254259 338298681547563005791 64615048178094058525454

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.383725.4.
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.bv_bjn$2$(not in LMFDB)