Properties

Label 2.17.ap_dm
Base field $\F_{17}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$
  $1 - 15 x + 90 x^{2} - 255 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0779791303774$, $\pm0.177280642489$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  1

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $110$ $71500$ $23703680$ $6978400000$ $2018018233550$

Point counts of the (virtual) curve

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

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{17}$.

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:

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)