# Properties

 Label 2.83.abe_ou 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: $1 - 30 x + 384 x^{2} - 2490 x^{3} + 6889 x^{4}$ Frobenius angles: $\pm0.0801876089965$, $\pm0.262835026667$ Angle rank: $2$ (numerical) Number field: 4.0.2900800.5 Galois group: $D_{4}$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=55x^6+15x^5+80x^4+40x^3+13x^2+56x+64$
• $y^2=22x^6+10x^5+11x^4+25x^3+14x^2+29x+31$
• $y^2=67x^6+70x^5+14x^4+42x^3+39x+27$
• $y^2=56x^6+16x^5+13x^4+12x^3+40x^2+49$
• $y^2=77x^6+17x^5+59x^4+4x^3+77x^2+26x+62$
• $y^2=17x^6+69x^5+59x^4+6x^3+78x^2+51x+6$
• $y^2=58x^6+3x^5+59x^4+77x^3+80x^2+49x+8$
• $y^2=50x^6+26x^5+71x^4+14x^3+31x^2+22x+48$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4754 46560676 326991667466 2252588556793936 15516162317924403914 106889896008114854003716 736365069753205810960642706 5072820188134591150546801996800 34946659076910001812623996204404034 240747534270345644705223431873360635396

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 54 6758 571878 47464566 3939071394 326940031622 27136043856738 2252292182936158 186940255467694374 15516041196697785878

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The endomorphism algebra of this simple isogeny class is 4.0.2900800.5.
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.be_ou $2$ (not in LMFDB)