Properties

Label 2.17.aj_cb
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:  $1 - 9 x + 53 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.261420712581$, $\pm0.365485551864$
Angle rank:  $2$ (numerical)
Number field:  4.0.51525.2
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
$A(\F_{q^r})$ 181 91405 25356109 7029501525 2015022786256 582376702681645 168366552246613909 48661206380169639525 14063098197814205215261 4064230740364296550912000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 315 5157 84163 1419174 24127395 410311197 6975759523 118587992409 2015993569950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.51525.2.
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_cb$2$(not in LMFDB)