# Properties

 Label 2.83.abe_ox 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: $( 1 - 17 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$ Frobenius angles: $\pm0.117184483028$, $\pm0.247123549255$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=62x^6+11x^5+57x^4+73x^3+57x^2+11x+62$
• $y^2=20x^6+57x^5+15x^4+33x^3+15x^2+57x+20$
• $y^2=23x^6+26x^5+33x^4+72x^3+7x^2+20x+57$
• $y^2=43x^6+59x^5+16x^4+6x^3+25x^2+27x+18$
• $y^2=18x^6+48x^5+x^4+29x^3+43x^2+38x+28$
• $y^2=52x^6+71x^5+50x^4+19x^3+50x^2+71x+52$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4757 46604329 327146653424 2252881645896361 15516538108163352557 106890250704441809403136 736365315281780918814022373 5072820295401368456891547456009 34946659075554323802361365784296176 240747534216889191307285836642250009849

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 54 6764 572148 47470740 3939166794 326941116518 27136052904798 2252292230561764 186940255460442444 15516041193252547964

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.ar $\times$ 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.ae_acd $2$ (not in LMFDB) 2.83.e_acd $2$ (not in LMFDB) 2.83.be_ox $2$ (not in LMFDB)