Properties

Label 2.83.abf_pq
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x + 83 x^{2} )( 1 - 15 x + 83 x^{2} )$
Frobenius angles:  $\pm0.158801688027$, $\pm0.192168636682$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4692 46450800 327083280048 2253050532216000 15516926384833852572 106890709028870480313600 736365660974636798757146028 5072820415094197157136069600000 34946658968426248849075365868351152 240747533971141735264540857171573654000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6741 572036 47474297 3939265363 326942518374 27136065644041 2252292283704433 186940254887381948 15516041177414264661

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.aq $\times$ 1.83.ap 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.ab_acw$2$(not in LMFDB)
2.83.b_acw$2$(not in LMFDB)
2.83.bf_pq$2$(not in LMFDB)