# Properties

 Label 2.83.abd_oj 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: $1 - 29 x + 373 x^{2} - 2407 x^{3} + 6889 x^{4}$ Frobenius angles: $\pm0.147367193729$, $\pm0.254584002254$ Angle rank: $2$ (numerical) Number field: 4.0.1911221.1 Galois group: $D_{4}$ Jacobians: 16

This isogeny class is simple and geometrically 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:

• $y^2=66x^6+66x^5+71x^4+54x^3+80x^2+25x+14$
• $y^2=76x^6+78x^5+69x^4+71x^3+45x^2+41x+10$
• $y^2=39x^6+59x^5+21x^4+71x^3+29x^2+62x+26$
• $y^2=48x^6+38x^5+72x^4+49x^3+6x^2+64x+17$
• $y^2=58x^6+3x^5+4x^4+35x^3+63x^2+13x+14$
• $y^2=60x^6+66x^5+60x^4+45x^3+80x^2+34x+72$
• $y^2=15x^6+41x^5+8x^4+22x^3+48x^2+16x+36$
• $y^2=47x^6+57x^5+77x^4+53x^3+73x^2+58x+47$
• $y^2=x^6+64x^4+40x^3+61x^2+41x+67$
• $y^2=40x^6+11x^5+49x^4+74x^3+64x^2+67x+42$
• $y^2=80x^6+37x^5+33x^4+x^3+30x^2+23x+6$
• $y^2=32x^6+47x^5+4x^4+26x^3+3x^2+14x+11$
• $y^2=59x^6+27x^5+39x^4+10x^3+24x^2+16x+62$
• $y^2=55x^6+9x^5+40x^4+60x^3+59x^2+76x+45$
• $y^2=14x^6+27x^5+36x^4+20x^3+12x^2+58x+67$
• $y^2=15x^6+60x^5+42x^4+71x^3+31x^2+56x+9$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4827 46817073 327422085741 2253126554551629 15516699636345046032 106890324886084018323825 736365325624310924440938393 5072820267472799619989192916789 34946659024817455128940162427314359 240747534150709945689729710860515395328

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 55 6795 572629 47475899 3939207800 326941343415 27136053285935 2252292218161699 186940255189035577 15516041188987333350

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The endomorphism algebra of this simple isogeny class is 4.0.1911221.1.
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.bd_oj $2$ (not in LMFDB)