Properties

Label 2.193.aby_bmw
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:  $( 1 - 26 x + 193 x^{2} )( 1 - 24 x + 193 x^{2} )$
Frobenius angles:  $\pm0.114714697559$, $\pm0.168091317575$
Angle rank:  $2$ (numerical)
Jacobians:  36

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 contains the Jacobians of 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28560 1369737600 51664941553680 1925162909429760000 71709211421119313302800 2671086154826010848925398400 99495248392843040480906060299920 3706098391523911012373494755164160000 138048458713905243850229098043590135505040 5142167038138670382342587055340555582531440000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36770 7186608 1387516798 267786328944 51682562939810 9974730658477008 1925122956902323198 371548729950161169744 71708904873470024818850

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.aba $\times$ 1.193.ay 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ac_aje$2$(not in LMFDB)
2.193.c_aje$2$(not in LMFDB)
2.193.by_bmw$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ac_aje$2$(not in LMFDB)
2.193.c_aje$2$(not in LMFDB)
2.193.by_bmw$2$(not in LMFDB)
2.193.abo_bcw$4$(not in LMFDB)
2.193.am_w$4$(not in LMFDB)
2.193.m_w$4$(not in LMFDB)
2.193.bo_bcw$4$(not in LMFDB)