Properties

Label 2.83.abe_or
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon base change
2.83.be_or$2$(not in LMFDB)