Properties

Label 2.193.abv_bjk
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 920 x^{2} - 9071 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.00969479075615$, $\pm0.256716224007$
Angle rank:  $2$ (numerical)
Number field:  4.0.42632.1
Galois group:  $D_{4}$
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 29052 1373810976 51673072637808 1925123348413800576 71708805180205990669692 2671084173077302902654246912 99495241528365330198470936844732 3706098373404858683839274351222358528 138048458678409336253148307271439635810416 5142167038096373452183452820253481216828381216

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 36881 7187742 1387488289 267784811907 51682524595166 9974729970290211 1925122947490429633 371548729854626170590 71708904872880182731121

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.42632.1.
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

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