Properties

Label 2.17.am_cp
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:  $1 - 12 x + 67 x^{2} - 204 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.112997812760$, $\pm0.326838618982$
Angle rank:  $2$ (numerical)
Number field:  4.0.58896.2
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 141 80793 24491700 6996108249 2015297698821 582512650102800 168380717002045269 48662715418390124649 14063246313837597011700 4064240468448309770809353

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 280 4986 83764 1419366 24133030 410345718 6975975844 118589241402 2015998395400

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.58896.2.
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.m_cp$2$(not in LMFDB)