Properties

Label 2.83.abf_po
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:  $( 1 - 17 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$
Frobenius angles:  $\pm0.117184483028$, $\pm0.221078141621$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4690 46421620 326976463240 2252839361735200 15516640638323543950 106890424321911650230720 736365460081722625580078590 5072820348876367185952809782400 34946659037200177672881638402340520 240747534131518565586257221576257642100

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6737 571850 47469849 3939192823 326941647554 27136058240869 2252292254304241 186940255255274510 15516041187750459857

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ar $\times$ 1.83.ao 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.ad_acu$2$(not in LMFDB)
2.83.d_acu$2$(not in LMFDB)
2.83.bf_po$2$(not in LMFDB)