Properties

Label 2.191.abw_bko
Base field $\F_{191}$
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:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 950 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0773520389145$, $\pm0.222263726252$
Angle rank:  $2$ (numerical)
Number field:  4.0.223488.6
Galois group:  $D_{4}$
Jacobians:  $56$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $28216$ $1316219968$ $48542199445624$ $1771233820354962432$ $64615199706685581252856$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $144$ $36078$ $6966576$ $1330890814$ $254195498064$ $48551231663214$ $9273284209474800$ $1771197284582068990$ $338298681544049898000$ $64615048177874524561518$

Jacobians and polarizations

This isogeny class contains the Jacobians of 56 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{191}$.

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.223488.6.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.191.bw_bko$2$(not in LMFDB)