Properties

Label 2.83.abg_qg
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:  $( 1 - 16 x + 83 x^{2} )^{2}$
Frobenius angles:  $\pm0.158801688027$, $\pm0.158801688027$
Angle rank:  $1$ (numerical)
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4624 46240000 326813448976 2252831296000000 15516830147685260944 106890747299335219360000 736365794338687930037512336 5072820581287523460473856000000 34946659110797977803551557216904464 240747534056326506412743217552996000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 52 6710 571564 47469678 3939240932 326942635430 27136070558684 2252292357492958 186940255648971412 15516041182904374550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.aq 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$
All geometric endomorphisms are defined over $\F_{83}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.a_adm$2$(not in LMFDB)
2.83.bg_qg$2$(not in LMFDB)
2.83.q_gr$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.a_adm$2$(not in LMFDB)
2.83.bg_qg$2$(not in LMFDB)
2.83.q_gr$3$(not in LMFDB)
2.83.a_dm$4$(not in LMFDB)
2.83.aq_gr$6$(not in LMFDB)