Properties

Label 2.83.abe_oz
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:  $1 - 30 x + 389 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.142946520854$, $\pm0.232154927040$
Angle rank:  $2$ (numerical)
Number field:  4.0.590400.4
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4759 46633441 327249988996 2253076095172041 15516782728097419039 106890468271837432652176 736365437766878761288262311 5072820298716888275866325534025 34946658984642507326210066724785764 240747534084939352117680232914609509521

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6768 572328 47474836 3939228894 326941781982 27136057418538 2252292232033828 186940254974127624 15516041184748456128

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.590400.4.
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.be_oz$2$(not in LMFDB)