Properties

Label 2.83.abc_nl
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:  $1 - 28 x + 349 x^{2} - 2324 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0829582297929$, $\pm0.306761272556$
Angle rank:  $2$ (numerical)
Number field:  4.0.834353.1
Galois group:  $D_{4}$
Jacobians:  34

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 34 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4887 46871217 327164085504 2252457124903449 15515857998623455047 106889677141140848590848 736365081259048087917468063 5072820373367084907375984783657 34946659270716188512074251953022208 240747534347690301745479906830583580497

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 56 6804 572180 47461796 3938994136 326939362182 27136044280744 2252292265177924 186940256504422316 15516041201682604884

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.834353.1.
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.bc_nl$2$(not in LMFDB)