Properties

Label 2.193.aca_bou
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:  $1 - 52 x + 1060 x^{2} - 10036 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0520524425611$, $\pm0.154252660331$
Angle rank:  $2$ (numerical)
Number field:  4.0.219392.2
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28222 1365888356 51644053293598 1925078071649230736 71708923936354747887742 2671085307268089832234712612 99495246183192836411225465758942 3706098386431087869179382872675422208 138048458703741253503660878781908471518366 5142167038122326586203290819485607547955262116

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 36666 7183702 1387455654 267785255382 51682546540506 9974730436952206 1925122954256869758 371548729922805430030 71708904873242106177946

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.219392.2.
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.ca_bou$2$(not in LMFDB)