Properties

Label 2.193.aby_bmv
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:  $1 - 50 x + 1009 x^{2} - 9650 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.100399071344$, $\pm0.177282845889$
Angle rank:  $2$ (numerical)
Number field:  4.0.1025600.4
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28559 1369661081 51663861696956 1925154636563717561 71709166299106868350239 2671085960833062954538395536 99495247709952045058537203475631 3706098389565423809415683789431613225 138048458709669179866760642179015877364284 5142167038134337154693937002930994109651742121

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36768 7186458 1387510836 267786160444 51682559186262 9974730590014908 1925122955884992228 371548729938760070394 71708904873409596791728

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.1025600.4.
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.by_bmv$2$(not in LMFDB)