Properties

Label 2.193.abw_bko
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:  $1 - 48 x + 950 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0484158406461$, $\pm0.235249588149$
Angle rank:  $2$ (numerical)
Number field:  4.0.223488.1
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28888 1372526656 51671151911704 1925139728722830336 71708939822334394340248 2671084747046999455173731392 99495243224346351430861583172184 3706098377024471399442883610134069248 138048458683997861331544807726236134956888 5142167038105890403566700086225741518220106816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36846 7187474 1387500094 267785314706 51682535700846 9974730140317970 1925122949370627838 371548729869667333778 71708904873012899182446

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.223488.1.
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.bw_bko$2$(not in LMFDB)