Properties

Label 2.211.acb_brc
Base field $\F_{211}$
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:  $\F_{211}$
Dimension:  $2$
L-polynomial:  $1 - 53 x + 1120 x^{2} - 11183 x^{3} + 44521 x^{4}$
Frobenius angles:  $\pm0.0585525127533$, $\pm0.181846139883$
Angle rank:  $2$ (numerical)
Number field:  4.0.2013752.2
Galois group:  $D_{4}$
Jacobians:  $8$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $34406$ $1956944468$ $88205127830024$ $3928782269701491872$ $174914183806045452700506$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $159$ $43953$ $9389586$ $1982111769$ $418227659389$ $88245949196514$ $18619893364855095$ $3928797478558913265$ $828976267921233207270$ $174913992534925959951793$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{211}$.

Endomorphism algebra over $\F_{211}$
The endomorphism algebra of this simple isogeny class is 4.0.2013752.2.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.211.cb_brc$2$(not in LMFDB)