# Properties

 Label 2.83.abe_or 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: $1 - 30 x + 381 x^{2} - 2490 x^{3} + 6889 x^{4}$ Frobenius angles: $\pm0.0255332992515$, $\pm0.274903135578$ Angle rank: $2$ (numerical) Number field: 4.0.654400.2 Galois group: $D_{4}$ Jacobians: 2

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 2 curves, and hence is principally polarizable:

• $y^2=52x^6+18x^5+43x^4+37x^3+33x^2+56x+72$
• $y^2=31x^6+69x^5+37x^4+56x^3+39x^2+47x+58$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4751 46517041 326836702244 2252293769242921 15515775895125056711 106889507203282083853456 736364749242902417205990959 5072819954444844396329117990025 34946658905043601364138243900380676 240747534124265195166954651225631912321

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 54 6752 571608 47458356 3938973294 326938842398 27136032045498 2252292079179748 186940254548328984 15516041187282984272

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The endomorphism algebra of this simple isogeny class is 4.0.654400.2.
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_or $2$ (not in LMFDB)