# Properties

 Label 2.83.abf_po 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: $( 1 - 17 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$ Frobenius angles: $\pm0.117184483028$, $\pm0.221078141621$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=26x^6+3x^5+17x^4+43x^3+76x^2+43x+42$
• $y^2=5x^6+48x^5+46x^4+14x^3+49x^2+54x+72$
• $y^2=28x^5+31x^4+60x^3+43x^2+81x+58$
• $y^2=29x^6+79x^5+24x^4+70x^3+63x^2+19x+2$
• $y^2=35x^6+50x^5+12x^4+62x^3+32x^2+49x+24$
• $y^2=57x^6+20x^5+64x^4+64x^3+23x^2+77x+43$
• $y^2=72x^6+9x^5+78x^4+x^3+40x^2+80x+23$
• $y^2=67x^6+20x^5+74x^4+21x^3+37x^2+75x+41$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4690 46421620 326976463240 2252839361735200 15516640638323543950 106890424321911650230720 736365460081722625580078590 5072820348876367185952809782400 34946659037200177672881638402340520 240747534131518565586257221576257642100

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 53 6737 571850 47469849 3939192823 326941647554 27136058240869 2252292254304241 186940255255274510 15516041187750459857

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.ar $\times$ 1.83.ao 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.ad_acu $2$ (not in LMFDB) 2.83.d_acu $2$ (not in LMFDB) 2.83.bf_po $2$ (not in LMFDB)