# Properties

 Label 2.83.abi_rm 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: $( 1 - 18 x + 83 x^{2} )( 1 - 16 x + 83 x^{2} )$ Frobenius angles: $\pm0.0496118990883$, $\pm0.158801688027$ 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:

• $y^2=3x^6+22x^5+27x^4+77x^3+9x^2+67x+37$
• $y^2=20x^6+12x^5+65x^4+50x^3+65x^2+12x+20$
• $y^2=82x^6+14x^5+37x^4+66x^3+21x^2+19x+34$
• $y^2=15x^6+32x^5+16x^4+73x^3+16x^2+32x+15$
• $y^2=59x^6+81x^5+79x^4+58x^3+39x^2+7x+11$
• $y^2=59x^6+62x^5+53x^4+9x^3+53x^2+62x+59$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4488 45777600 326105714088 2252030863104000 15516083908976100648 106890155549597681553600 736365398329616192701344264 5072820372079047273622007808000 34946659048106973526059723129970632 240747534088207128988090939043680248000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 50 6642 570326 47452814 3939051490 326940825474 27136055965222 2252292264606046 186940255313618258 15516041184959062482

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.as $\times$ 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.ac_aes $2$ (not in LMFDB) 2.83.c_aes $2$ (not in LMFDB) 2.83.bi_rm $2$ (not in LMFDB)