Properties

Label 2.17.aj_cc
Base Field $\F_{17}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $( 1 - 5 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$
Frobenius angles:  $\pm0.292637436158$, $\pm0.338793663197$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 182 92092 25492376 7038775744 2014450139702 582215684866816 168354868337287814 48661349247531820800 14063198471181701378264 4064238953138390667693052

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 317 5184 84273 1418769 24120722 410282721 6975780001 118588837968 2015997643757

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.af $\times$ 1.17.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_o$2$(not in LMFDB)
2.17.b_o$2$(not in LMFDB)
2.17.j_cc$2$(not in LMFDB)