Properties

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

Learn more about

Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $1 - 29 x + 369 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.107448708646$, $\pm0.275598886837$
Angle rank:  $2$ (numerical)
Number field:  4.0.5897933.1
Galois group:  $D_{4}$
Jacobians:  19

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 19 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4823 46758985 327222372113 2252769576000125 15516283824919307248 106889998411112772513385 736365188812273872199901189 5072820321229502643924105927125 34946659190327794982957837369094587 240747534330018668119344800560745516800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6787 572281 47468379 3939102240 326940344839 27136048244227 2252292242029251 186940256074400473 15516041200543678182

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.5897933.1.
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.
TwistExtension DegreeCommon base change
2.83.bd_of$2$(not in LMFDB)