# Properties

 Label 2.17.aj_by Base Field $\F_{17}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## 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:

• $y^2=7x^6+7x^5+13x^4+16x^3+3x^2+11x+1$
• $y^2=3x^6+10x^5+14x^4+5x^3+2x^2+5x+11$
• $y^2=6x^6+15x^5+16x^4+6x^2+12x+16$
• $y^2=10x^6+9x^5+9x^4+9x^3+4x^2+10x+16$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 178 89356 24949192 6999791616 2015978331058 582739674698752 168394782386517298 48661501261692100608 14062975351879497100744 4064220154548700275695116

 $r$ 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.
 Twist Extension Degree Common base change 2.17.j_by $2$ (not in LMFDB)