Properties

Label 2.83.abf_pp
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:  $1 - 31 x + 405 x^{2} - 2573 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.134511996275$, $\pm0.210436945261$
Angle rank:  $2$ (numerical)
Number field:  4.0.174725.2
Galois group:  $D_{4}$
Jacobians:  6

This isogeny class is simple and geometrically 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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4691 46436209 327029870429 2252945041254701 15516784121925902416 106890568708587142957921 736365565180104953892300041 5072820390129754449515077814069 34946659014273523784978322463168991 240747534064501381929807662294525281024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6739 571943 47472075 3939229248 326942089183 27136062113885 2252292272620419 186940255132632899 15516041183431240614

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.174725.2.
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.bf_pp$2$(not in LMFDB)