Properties

Label 2.191.abw_bkp
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:  $1 - 48 x + 951 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0856585252156$, $\pm0.218971105078$
Angle rank:  $2$ (numerical)
Number field:  4.0.13040272.1
Galois group:  $D_{4}$
Jacobians:  $16$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $28217$ $1316294833$ $48543204099908$ $1771241026132892713$ $64615235944826395314857$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $144$ $36080$ $6966720$ $1330896228$ $254195640624$ $48551234577158$ $9273284257555728$ $1771197285222884164$ $338298681550606970688$ $64615048177915421324240$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 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 4.0.13040272.1.

Base change

This is a primitive isogeny class.

Twists

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

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