Properties

Label 2.193.acb_bpw
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $( 1 - 27 x + 193 x^{2} )( 1 - 26 x + 193 x^{2} )$
Frobenius angles:  $\pm0.0758389534121$, $\pm0.114714697559$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28056 1364082720 51635318652288 1925049761953718400 71708865687914240527896 2671085307370930312446904320 99495246892347096065464184109912 3706098390777728740262530482400780800 138048458722253713680162453500685725089152 5142167038187204629222796458466871500708493600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 141 36617 7182486 1387435249 267785037861 51682546542494 9974730508047285 1925122956514720801 371548729972630550358 71708904874146847968857

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.abb $\times$ 1.193.aba and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_ame$2$(not in LMFDB)
2.193.b_ame$2$(not in LMFDB)
2.193.cb_bpw$2$(not in LMFDB)