Properties

Label 2.17.ao_de
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.240632536990$
Angle rank:  $2$ (numerical)
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 120 74880 24069240 6996787200 2017565556600 582640049047680 168371111648329080 48660500749182566400 14063061977523943296120 4064234154788176529846400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 258 4900 83774 1420964 24138306 410322308 6975658366 118587686980 2015995263618

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ai $\times$ 1.17.ag 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.ac_ao$2$(not in LMFDB)
2.17.c_ao$2$(not in LMFDB)
2.17.o_de$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ac_ao$2$(not in LMFDB)
2.17.c_ao$2$(not in LMFDB)
2.17.o_de$2$(not in LMFDB)
2.17.ai_bu$4$(not in LMFDB)
2.17.ae_w$4$(not in LMFDB)
2.17.e_w$4$(not in LMFDB)
2.17.i_bu$4$(not in LMFDB)