Properties

Label 2.83.abf_pm
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:  $1 - 31 x + 402 x^{2} - 2573 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0858905147336$, $\pm0.235991757082$
Angle rank:  $2$ (numerical)
Number field:  4.0.258077.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4688 46392448 326869656128 2252627436982784 15516350009006779888 106890123333677620934656 736365221832077478975431984 5072820216846421863865501534208 34946659012202030812207855857054272 240747534181417306203857126308866498688

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6733 571664 47465385 3939119043 326940726934 27136049461049 2252292195683985 186940255121551856 15516041190966405213

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.258077.1.
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.bf_pm$2$(not in LMFDB)