Properties

Label 2.193.abx_blq
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:  $1 - 49 x + 978 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0549247165904$, $\pm0.216032287700$
Angle rank:  $2$ (numerical)
Number field:  4.0.7540236.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28722 1371015948 51666339579336 1925137335886408704 71708993036323845168882 2671085062389232685249740800 99495244292660060367489895051698 3706098379333666796779308738555654144 138048458685872388295481042495765884394184 5142167038097249931799228255258737997414454028

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36805 7186804 1387498369 267785513425 51682541802370 9974730247419985 1925122950570133249 371548729874712505012 71708904872892405475525

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.7540236.1.
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_blq$2$(not in LMFDB)