Properties

Label 2.17.aj_bv
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:  $1 - 9 x + 47 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.162674028495$, $\pm0.429661290527$
Angle rank:  $2$ (numerical)
Number field:  4.0.10933.1
Galois group:  $D_{4}$
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 175 87325 24544975 6967225125 2015788054000 582916328592325 168409518913049575 48662100757270657125 14063019009180656508175 4064225772894002499616000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 303 4995 83419 1419714 24149751 410415903 6975887731 118587324645 2015991105918

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.10933.1.
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.j_bv$2$(not in LMFDB)