# Properties

 Label 2.17.aj_bw 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: $( 1 - 7 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$ Frobenius angles: $\pm0.177280642489$, $\pm0.422020869623$ Angle rank: $2$ (numerical) Jacobians: 7

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 7 curves, and hence is principally polarizable:

• $y^2=2x^6+x^5+5x^4+13x^3+11x^2+9x+7$
• $y^2=11x^5+8x^4+16x^3+8x^2+11$
• $y^2=5x^6+12x^5+13x^4+2x^3+16x^2+7x+15$
• $y^2=14x^6+3x^5+12x^4+3x^3+7x^2+14x+4$
• $y^2=9x^6+6x^5+8x^4+x^3+4x^2+4x+14$
• $y^2=12x^6+x^5+12x^4+8x^2+14x+10$
• $y^2=9x^6+3x^5+13x^3+2x^2+15x+14$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 176 88000 24679424 6978400000 2015978955056 582878636032000 168406364743212464 48661929864662400000 14062994505410958119936 4064222670497930690200000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 305 5022 83553 1419849 24148190 410408217 6975863233 118587118014 2015989567025

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ah $\times$ 1.17.ac 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.af_u $2$ (not in LMFDB) 2.17.f_u $2$ (not in LMFDB) 2.17.j_bw $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.af_u $2$ (not in LMFDB) 2.17.f_u $2$ (not in LMFDB) 2.17.j_bw $2$ (not in LMFDB) 2.17.ap_dm $4$ (not in LMFDB) 2.17.ab_aw $4$ (not in LMFDB) 2.17.b_aw $4$ (not in LMFDB) 2.17.p_dm $4$ (not in LMFDB)