Properties

Label 2.193.abw_bkp
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:  $1 - 48 x + 951 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0585217950236$, $\pm0.232730388834$
Angle rank:  $2$ (numerical)
Number field:  4.0.17193616.1
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
$A(\F_{q^r})$ 28889 1372603057 51672188400644 1925147241039838249 71708978126421636040649 2671084900266717910685268496 99495243732381546539325676357097 3706098378475410766769590423387694025 138048458687736515680424913571597015028996 5142167038115298028657570317956440989062360977

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36848 7187618 1387505508 267785457746 51682538665478 9974730191250194 1925122950124314436 371548729879729686434 71708904873144091049168

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.17193616.1.
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.bw_bkp$2$(not in LMFDB)