# Properties

 Label 2.83.abd_og 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: $( 1 - 17 x + 83 x^{2} )( 1 - 12 x + 83 x^{2} )$ Frobenius angles: $\pm0.117184483028$, $\pm0.271155063531$ Angle rank: $2$ (numerical) Jacobians: 30

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 30 curves, and hence is principally polarizable:

• $y^2=11x^6+11x^5+70x^4+69x^3+39x^2+32x+75$
• $y^2=27x^6+40x^5+67x^4+43x^3+36x^2+47x+18$
• $y^2=82x^6+25x^5+66x^4+28x^3+69x^2+39x+34$
• $y^2=74x^6+66x^5+43x^4+36x^3+3x^2+49x+6$
• $y^2=56x^6+13x^5+29x^4+25x^3+3x^2+17x+12$
• $y^2=30x^6+72x^5+64x^4+53x^3+32x^2+33x+18$
• $y^2=54x^6+22x^5+32x^4+15x^3+66x^2+9x+56$
• $y^2=75x^6+27x^5+17x^4+71x^3+73x^2+48x+20$
• $y^2=63x^6+45x^5+66x^4+20x^3+17x^2+11x+25$
• $y^2=4x^6+60x^5+59x^3+54x^2+39x+18$
• $y^2=70x^6+19x^5+3x^4+37x^3+40x^2+29x+67$
• $y^2=56x^6+9x^5+48x^4+7x^3+21x^2+39$
• $y^2=5x^6+78x^5+82x^4+57x^3+8x^2+35x+75$
• $y^2=72x^6+26x^5+12x^4+51x^3+75x^2+47x+20$
• $y^2=51x^6+19x^5+17x^4+65x^3+82x^2+60x+5$
• $y^2=6x^6+55x^5+6x^4+59x^3+3x^2+26x+15$
• $y^2=8x^6+69x^5+65x^4+58x^3+10x^2+7x+1$
• $y^2=18x^6+82x^5+71x^4+58x^3+35x^2+64x+43$
• $y^2=45x^6+71x^5+63x^4+52x^3+43x^2+7x+30$
• $y^2=59x^6+52x^5+47x^4+74x^3+3x^2+33x+38$
• $y^2=3x^6+81x^5+58x^4+41x^3+9x^2+36x+76$
• $y^2=77x^6+12x^5+71x^4+8x^3+6x^2+44x+2$
• $y^2=x^6+44x^5+76x^4+25x^3+39x^2+28x+71$
• $y^2=5x^6+68x^5+56x^4+55x^3+12x^2+10x+82$
• $y^2=22x^6+81x^5+15x^4+59x^3+30x^2+17x+31$
• $y^2=41x^6+5x^5+16x^4+59x^3+6x^2+14x+21$
• $y^2=17x^6+11x^5+27x^4+76x^3+80x^2+10x+56$
• $y^2=22x^6+28x^5+30x^4+52x^3+25x^2+25x+60$
• $y^2=61x^6+13x^5+50x^4+67x^3+40x^2+48x+24$
• $y^2=32x^6+26x^5+41x^4+17x^3+47x^2+34x+19$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4824 46773504 327272297184 2252859103835136 15516389490835992264 106890085272268210139136 736365233806656885327818664 5072820324354417375805014134784 34946659168675355889055530470236896 240747534303309562832601390300720340224

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 55 6789 572368 47470265 3939129065 326940610518 27136049902331 2252292243416689 186940255958575024 15516041198822291589

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The isogeny class factors as 1.83.ar $\times$ 1.83.am 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.af_abm $2$ (not in LMFDB) 2.83.f_abm $2$ (not in LMFDB) 2.83.bd_og $2$ (not in LMFDB)