Properties

Label 2.193.aby_bmt
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:  $( 1 - 27 x + 193 x^{2} )( 1 - 23 x + 193 x^{2} )$
Frobenius angles:  $\pm0.0758389534121$, $\pm0.189598946136$
Angle rank:  $2$ (numerical)
Jacobians:  26

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 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28557 1369508049 51661702001664 1925138074205929401 71709075653424180319557 2671085567746732480095338496 99495246298778054404532289871893 3706098385331371097843764156062122409 138048458699354185953771849657436052468736 5142167038116457419607927719289613476271697249

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36764 7186158 1387498900 267785821944 51682551580478 9974730448540008 1925122953685624804 371548729910997914094 71708904873160259068364

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.abb $\times$ 1.193.ax 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.ae_ajb$2$(not in LMFDB)
2.193.e_ajb$2$(not in LMFDB)
2.193.by_bmt$2$(not in LMFDB)
2.193.abd_qy$3$(not in LMFDB)
2.193.ac_ald$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ae_ajb$2$(not in LMFDB)
2.193.e_ajb$2$(not in LMFDB)
2.193.by_bmt$2$(not in LMFDB)
2.193.abd_qy$3$(not in LMFDB)
2.193.ac_ald$3$(not in LMFDB)
2.193.aca_bov$6$(not in LMFDB)
2.193.az_mu$6$(not in LMFDB)
2.193.c_ald$6$(not in LMFDB)
2.193.z_mu$6$(not in LMFDB)
2.193.bd_qy$6$(not in LMFDB)
2.193.ca_bov$6$(not in LMFDB)