Properties

Label 2.83.abh_qw
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:  $( 1 - 17 x + 83 x^{2} )( 1 - 16 x + 83 x^{2} )$
Frobenius angles:  $\pm0.117184483028$, $\pm0.158801688027$
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
$A(\F_{q^r})$ 4556 46015600 326488737008 2252497671544000 15516567521229784196 106890600222737815993600 736365767668580455434545012 5072820649789829172186076128000 34946659234421190371019141667346672 240747534194549281977435597248587798000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 51 6677 570996 47462649 3939174261 326942185574 27136069575855 2252292387907441 186940256310269388 15516041191812753557

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ar $\times$ 1.83.aq 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_aec$2$(not in LMFDB)
2.83.b_aec$2$(not in LMFDB)
2.83.bh_qw$2$(not in LMFDB)