Properties

Label 2.193.abx_blr
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:  $1 - 49 x + 979 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0658427939180$, $\pm0.212731672563$
Angle rank:  $2$ (numerical)
Number field:  4.0.8118173.3
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28723 1371092405 51667397741323 1925145231237101525 71709034828356638905648 2671085237179036090366085405 99495244900473463934797616278219 3706098381138604942296595410211777925 138048458690529400659949250917177165566427 5142167038107929240983797021167086693144454400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36807 7186951 1387504059 267785669490 51682545184359 9974730308355307 1925122951507703571 371548729887246560413 71708904873041331319582

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.8118173.3.
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.bx_blr$2$(not in LMFDB)