# Properties

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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4556 46015600 326488737008 2252497671544000 15516567521229784196 106890600222737815993600 736365767668580455434545012 5072820649789829172186076128000 34946659234421190371019141667346672 240747534194549281977435597248587798000

 $r$ 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.
 Twist Extension Degree Common 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)