Properties

Label 2.17.am_co
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:  $( 1 - 8 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.338793663197$
Angle rank:  $2$ (numerical)
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 140 80080 24309740 6970163200 2012913910700 582362478377680 168373686149659340 48662349062661734400 14063213539280935740620 4064237789427522323016400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 278 4950 83454 1417686 24126806 410328582 6975923326 118588965030 2015997066518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ai $\times$ 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ae_c$2$(not in LMFDB)
2.17.e_c$2$(not in LMFDB)
2.17.m_co$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.ae_c$2$(not in LMFDB)
2.17.e_c$2$(not in LMFDB)
2.17.m_co$2$(not in LMFDB)
2.17.ag_bq$4$(not in LMFDB)
2.17.ac_ba$4$(not in LMFDB)
2.17.c_ba$4$(not in LMFDB)
2.17.g_bq$4$(not in LMFDB)