# Properties

 Label 2.83.abg_qc 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: $( 1 - 18 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$ Frobenius angles: $\pm0.0496118990883$, $\pm0.221078141621$ Angle rank: $2$ (numerical) Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=13x^6+52x^5+48x^4+73x^3+3x^2+29x+19$
• $y^2=22x^6+42x^5+60x^4+33x^3+2x^2+67x+54$
• $y^2=47x^6+52x^5+35x^4+4x^3+62x^2+19x+42$
• $y^2=80x^6+48x^5+79x^4+75x^3+31x^2+29x+35$
• $y^2=45x^6+22x^5+4x^4+50x^3+38x^2+35x+18$
• $y^2=43x^6+72x^5+18x^4+70x^3+67x^2+20x+15$
• $y^2=18x^6+28x^5+7x^4+10x^3+7x^2+28x+18$
• $y^2=80x^6+38x^5+20x^4+8x^3+20x^2+38x+80$
• $y^2=64x^6+65x^5+x^4+58x^3+82x^2+46x+56$
• $y^2=48x^6+54x^5+64x^4+64x^3+64x^2+54x+48$
• $y^2=76x^6+15x^5+62x^4+60x^3+6x^2+34x+15$
• $y^2=39x^6+34x^5+65x^4+44x^3+36x^2+58x+28$
• $y^2=46x^6+65x^5+18x^4+64x^3+18x^2+65x+46$
• $y^2=37x^6+24x^5+22x^4+20x^3+45x^2+70x+56$
• $y^2=67x^6+34x^5+9x^4+67x^3+72x^2+47x+45$
• $y^2=55x^6+67x^5+66x^4+9x^3+52x^2+14x+52$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4620 46181520 326592868140 2252372482483200 15516157023790985100 106889979649503276792720 736365090742912639181383980 5072820071165601760849677926400 34946658850885961879384057167876620 240747534025176412624754269447068819600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 52 6702 571180 47460014 3939070052 326940287454 27136044630236 2252292131002846 186940254258623380 15516041180896768782

## Decomposition and endomorphism algebra

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