Properties

Label 2.83.abi_rm
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:  $( 1 - 18 x + 83 x^{2} )( 1 - 16 x + 83 x^{2} )$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.158801688027$
Angle rank:  $2$ (numerical)
Jacobians:  6

This isogeny class is not 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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4488 45777600 326105714088 2252030863104000 15516083908976100648 106890155549597681553600 736365398329616192701344264 5072820372079047273622007808000 34946659048106973526059723129970632 240747534088207128988090939043680248000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 50 6642 570326 47452814 3939051490 326940825474 27136055965222 2252292264606046 186940255313618258 15516041184959062482

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as $\times$ 1.83.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_aes$2$(not in LMFDB)
2.83.c_aes$2$(not in LMFDB)
2.83.bi_rm$2$(not in LMFDB)