# Properties

 Label 2.17.am_co 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: $( 1 - 8 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ Frobenius angles: $\pm0.0779791303774$, $\pm0.338793663197$ Angle rank: $2$ (numerical) Jacobians: 4

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 4 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 140 80080 24309740 6970163200 2012913910700 582362478377680 168373686149659340 48662349062661734400 14063213539280935740620 4064237789427522323016400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 278 4950 83454 1417686 24126806 410328582 6975923326 118588965030 2015997066518

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ai $\times$ 1.17.ae 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ae_c $2$ (not in LMFDB) 2.17.e_c $2$ (not in LMFDB) 2.17.m_co $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.ae_c $2$ (not in LMFDB) 2.17.e_c $2$ (not in LMFDB) 2.17.m_co $2$ (not in LMFDB) 2.17.ag_bq $4$ (not in LMFDB) 2.17.ac_ba $4$ (not in LMFDB) 2.17.c_ba $4$ (not in LMFDB) 2.17.g_bq $4$ (not in LMFDB)