Properties

Label 2.193.abw_bko
Base field $\F_{193}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
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, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $28888$ $1372526656$ $51671151911704$ $1925139728722830336$ $71708939822334394340248$

Point counts of the curve

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

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{193}$.

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.223488.1.

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)