Properties

Label 2.17.am_cr
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:  $( 1 - 7 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$
Frobenius angles:  $\pm0.177280642489$, $\pm0.292637436158$
Angle rank:  $2$ (numerical)
Jacobians:  3

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 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
$A(\F_{q^r})$ 143 82225 24856832 7047093625 2019558358103 582683913011200 168373478252203367 48660930058145315625 14063093622411016671488 4064232651550128628338625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 284 5058 84372 1422366 24140126 410328078 6975719908 118587953826 2015994517964

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ah $\times$ 1.17.af 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.ac_ab$2$(not in LMFDB)
2.17.c_ab$2$(not in LMFDB)
2.17.m_cr$2$(not in LMFDB)