Properties

Label 2.17.ap_dm
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.177280642489$
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
$A(\F_{q^r})$ 110 71500 23703680 6978400000 2018018233550 582830824576000 168392298144692270 48661929864662400000 14063108690397910183040 4064231487841064613287500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 245 4824 83553 1421283 24146210 410373939 6975863233 118588080888 2015993940725

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ai $\times$ 1.17.ah 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ab_aw$2$(not in LMFDB)
2.17.b_aw$2$(not in LMFDB)
2.17.p_dm$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ab_aw$2$(not in LMFDB)
2.17.b_aw$2$(not in LMFDB)
2.17.p_dm$2$(not in LMFDB)
2.17.aj_bw$4$(not in LMFDB)
2.17.af_u$4$(not in LMFDB)
2.17.f_u$4$(not in LMFDB)
2.17.j_bw$4$(not in LMFDB)