# Properties

 Label 2.83.abf_pq 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: $( 1 - 16 x + 83 x^{2} )( 1 - 15 x + 83 x^{2} )$ 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)