Properties

Label 2.83.abd_ob
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:  $1 - 29 x + 365 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0639743454557$, $\pm0.290481692689$
Angle rank:  $2$ (numerical)
Number field:  4.0.68725.1
Galois group:  $D_{4}$
Jacobians:  15

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 15 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4819 46700929 327022693909 2252409576442861 15515849740694096464 106889615912389102305601 736364936010853492417512049 5072820194517998500391546374389 34946659134434441428008093278088991 240747534291837328195923038682528481024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6779 571933 47460795 3938992040 326939174903 27136038928151 2252292185770339 186940255775410009 15516041198082912614

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.68725.1.
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_ob$2$(not in LMFDB)