Properties

 Label 2.83.abc_ni 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: $( 1 - 18 x + 83 x^{2} )( 1 - 10 x + 83 x^{2} )$ Frobenius angles: $\pm0.0496118990883$, $\pm0.315076740302$ 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:

• $y^2=35x^6+15x^5+76x^4+24x^3+76x^2+15x+35$
• $y^2=42x^6+50x^5+37x^4+30x^3+5x^2+48x+72$
• $y^2=66x^6+46x^5+69x^4+65x^3+3x^2+20x+12$
• $y^2=2x^6+14x^5+43x^4+24x^3+31x^2+14x+72$
• $y^2=6x^6+23x^5+79x^4+38x^3+73x^2+64x+79$
• $y^2=53x^6+13x^5+45x^4+39x^3+71x^2+59x+71$
• $y^2=55x^6+48x^5+14x^4+4x^3+37x^2+24x+42$
• $y^2=42x^6+44x^5+5x^4+26x^3+5x^2+44x+42$
• $y^2=42x^6+37x^5+60x^4+45x^3+77x^2+16x+35$
• $y^2=65x^6+32x^5+78x^4+78x^3+6x^2+21x+2$
• $y^2=8x^6+16x^5+71x^4+21x^3+16x^2+47x+42$
• $y^2=2x^6+71x^5+81x^4+4x^3+72x^2+57x+6$
• $y^2=50x^6+65x^5+47x^4+8x^3+18x^2+37x+56$
• $y^2=34x^6+35x^5+77x^4+43x^3+77x^2+35x+34$
• $y^2=47x^6+67x^5+61x^4+62x^3+54x^2+29x+57$
• $y^2=8x^6+54x^5+78x^4+20x^3+25x^2+40x+9$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4884 46827792 327019555764 2252208505181184 15515573444515367124 106889433811913573534736 736364907019614503009330292 5072820244747059012882175180800 34946659153045064323820174053169556 240747534230357623274324477578046279952

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 56 6798 571928 47456558 3938921896 326938617918 27136037859784 2252292208071646 186940255874963864 15516041194120580718

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.as $\times$ 1.83.ak 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.ai_ao $2$ (not in LMFDB) 2.83.i_ao $2$ (not in LMFDB) 2.83.bc_ni $2$ (not in LMFDB)