# Properties

 Label 2.83.abd_oe 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: $1 - 29 x + 368 x^{2} - 2407 x^{3} + 6889 x^{4}$ Frobenius angles: $\pm0.0975278333375$, $\pm0.279698317393$ Angle rank: $2$ (numerical) Number field: 4.0.6473016.1 Galois group: $D_{4}$ Jacobians: 12

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 12 curves, and hence is principally polarizable:

• $y^2=55x^6+2x^4+59x^3+78x^2+13x+28$
• $y^2=76x^6+21x^5+69x^4+x^3+51x^2+42x+21$
• $y^2=24x^6+55x^5+27x^4+65x^3+78x^2+3x+52$
• $y^2=14x^6+62x^5+80x^4+43x^3+31x^2+7x+72$
• $y^2=52x^6+72x^5+69x^4+82x^3+52x^2+2x+63$
• $y^2=18x^6+30x^5+68x^4+44x^3+58x^2+65x+27$
• $y^2=7x^6+37x^5+81x^4+5x^3+3x^2+35x+53$
• $y^2=80x^6+3x^5+54x^4+69x^3+31x^2+46x+6$
• $y^2=68x^6+62x^5+14x^4+64x^3+54x^2+61x+56$
• $y^2=22x^6+52x^4+32x^3+53x^2+64x+53$
• $y^2=16x^6+47x^5+62x^4+58x^3+76x^2+53x+57$
• $y^2=16x^6+65x^5+75x^4+67x^3+11x^2+54x+18$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4822 46744468 327172449256 2252679859352224 15516177016952599882 106889908048472760894400 736365136568554375624735258 5072820306825460091954388983424 34946659198143966978246324635040904 240747534343142713625632643047878814228

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 55 6785 572194 47466489 3939075125 326940068450 27136046318975 2252292235633969 186940256116211542 15516041201389515425

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The endomorphism algebra of this simple isogeny class is 4.0.6473016.1.
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_oe $2$ (not in LMFDB)