Properties

Label 2.17.aj_by
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:  $1 - 9 x + 50 x^{2} - 153 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.207100498588$, $\pm0.404445408663$
Angle rank:  $2$ (numerical)
Number field:  4.0.447372.1
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
$A(\F_{q^r})$ 178 89356 24949192 6999791616 2015978331058 582739674698752 168394782386517298 48661501261692100608 14062975351879497100744 4064220154548700275695116

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 309 5076 83809 1419849 24142434 410379993 6975801793 118586956500 2015988319029

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The endomorphism algebra of this simple isogeny class is 4.0.447372.1.
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_by$2$(not in LMFDB)