# Properties

 Label 2.83.abf_pk Base Field $\F_{83}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{83}$ Dimension: $2$ L-polynomial: $( 1 - 18 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$ Frobenius angles: $\pm0.0496118990883$, $\pm0.247123549255$ Angle rank: $2$ (numerical) Jacobians: 3

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 contains the Jacobians of 3 curves, and hence is principally polarizable:

• $y^2=75x^6+35x^5+82x^4+6x^3+20x^2+72x+16$
• $y^2=19x^6+13x^5+77x^4+73x^3+44x^2+21x+52$
• $y^2=42x^6+71x^5+27x^4+72x^3+77x^2+x+32$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4686 46363284 326762858664 2252414757881376 15516054496826400066 106889806032755698028736 736364945943043559719370706 5072820017690605959268950455424 34946658889240107804382931288966856 240747534110547038308073272360251642324

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 53 6729 571478 47460905 3939044023 326939756418 27136039294165 2252292107260369 186940254463791314 15516041186398856889

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.as $\times$ 1.83.an 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.af_acq $2$ (not in LMFDB) 2.83.f_acq $2$ (not in LMFDB) 2.83.bf_pk $2$ (not in LMFDB)