Properties

Label 2.17.aj_bu
Base Field $\F_{17}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $1 - 9 x + 46 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.147872872551$, $\pm0.436753511906$
Angle rank:  $2$ (numerical)
Number field:  4.0.971388.2
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 174 86652 24410808 6955729344 2015469561774 582932438477568 168410708192052318 48662191704444602112 14063046087231918221688 4064229474706288087398972

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 301 4968 83281 1419489 24150418 410418801 6975900769 118587552984 2015992942141

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.971388.2.
All geometric endomorphisms are defined over $\F_{17}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.j_bu$2$(not in LMFDB)