Properties

Label 2.83.abd_nz
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:  $1 - 29 x + 363 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0299902267827$, $\pm0.296749112487$
Angle rank:  $2$ (numerical)
Number field:  4.0.1766861.2
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:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4817 46671913 326922867971 2252228443610669 15515625846165633232 106889403575608118981425 736364765453077763219366423 5072820060644453681138543132309 34946659015168791814714629413358749 240747534172788875051427721257070736128

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6775 571759 47456979 3938935200 326938525435 27136032642865 2252292126331539 186940255137421957 15516041190410307750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.1766861.2.
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.bd_nz$2$(not in LMFDB)