Properties

Label 2.17.ai_bh
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:  $1 - 8 x + 33 x^{2} - 136 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.0550704494671$, $\pm0.504752145218$
Angle rank:  $2$ (numerical)
Number field:  4.0.39593.1
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 179 83593 23519168 6890821769 2014054099699 582738000449536 168370241098946387 48659818633199903753 14063094273277609256384 4064237975893985628512713

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 292 4786 82500 1418490 24142366 410320186 6975560580 118587959314 2015997159012

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.39593.1.
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.i_bh$2$(not in LMFDB)