# Properties

 Label 2.17.am_cr 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: $( 1 - 7 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ Frobenius angles: $\pm0.177280642489$, $\pm0.292637436158$ Angle rank: $2$ (numerical) Jacobians: 3

This isogeny class is not 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 3 curves, and hence is principally polarizable:

• $y^2=11x^6+11x^4+14x^3+11x^2+11$
• $y^2=6x^6+2x^5+13x^4+15x^3+13x^2+2x+6$
• $y^2=14x^6+3x^5+14x^4+12x^3+14x^2+3x+14$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 143 82225 24856832 7047093625 2019558358103 582683913011200 168373478252203367 48660930058145315625 14063093622411016671488 4064232651550128628338625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 284 5058 84372 1422366 24140126 410328078 6975719908 118587953826 2015994517964

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ah $\times$ 1.17.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_ab $2$ (not in LMFDB) 2.17.c_ab $2$ (not in LMFDB) 2.17.m_cr $2$ (not in LMFDB)