Properties

Label 2.17.al_cl
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:  $1 - 11 x + 63 x^{2} - 187 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.203473685038$, $\pm0.321669352104$
Angle rank:  $2$ (numerical)
Number field:  4.0.29525.1
Galois group:  $D_{4}$
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 155 85405 25072955 7046339525 2018243902000 582573093106645 168370049959276355 48661002711561767525 14063091259929107805755 4064230164591533262112000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 295 5101 84363 1421442 24135535 410319721 6975730323 118587933907 2015993284350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.29525.1.
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.l_cl$2$(not in LMFDB)