Properties

Label 2.193.aby_bms
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:  $1 - 50 x + 1006 x^{2} - 9650 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0633713900940$, $\pm0.194366849898$
Angle rank:  $2$ (numerical)
Number field:  4.0.191600.1
Galois group:  $D_{4}$
Jacobians:  $24$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $28556$ $1369431536$ $51660622163084$ $1925129784714135296$ $71709030129753846498636$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $144$ $36762$ $7186008$ $1387492926$ $267785651944$ $51682547728218$ $9974730375523008$ $1925122952503205118$ $371548729894612587744$ $71708904872970152386522$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 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 4.0.191600.1.

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.by_bms$2$(not in LMFDB)