Properties

Label 2.83.abd_oa
Base field $\F_{83}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 18 x + 83 x^{2} )( 1 - 11 x + 83 x^{2} )$
  $1 - 29 x + 364 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.293691115068$
Angle rank:  $2$ (numerical)
Jacobians:  $12$
Isomorphism classes:  75

This isogeny class is not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4818$ $46686420$ $326972779848$ $2252319104455200$ $15515738364469272798$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $55$ $6777$ $571846$ $47458889$ $3938963765$ $326938855554$ $27136035922127$ $2252292158712721$ $186940255498983778$ $15516041194833651657$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83}$.

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as $\times$ 1.83.al and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.83.ah_abg$2$(not in LMFDB)
2.83.h_abg$2$(not in LMFDB)
2.83.bd_oa$2$(not in LMFDB)