Properties

Label 2.83.abf_pk
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 18 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.247123549255$
Angle rank:  $2$ (numerical)
Jacobians:  3

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4686 46363284 326762858664 2252414757881376 15516054496826400066 106889806032755698028736 736364945943043559719370706 5072820017690605959268950455424 34946658889240107804382931288966856 240747534110547038308073272360251642324

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6729 571478 47460905 3939044023 326939756418 27136039294165 2252292107260369 186940254463791314 15516041186398856889

Decomposition and endomorphism algebra

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

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.af_acq$2$(not in LMFDB)
2.83.f_acq$2$(not in LMFDB)
2.83.bf_pk$2$(not in LMFDB)