Properties

 Label 2.17.am_cs 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: $( 1 - 6 x + 17 x^{2} )^{2}$ Frobenius angles: $\pm0.240632536990$, $\pm0.240632536990$ Angle rank: $1$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 144 82944 25040016 7072137216 2021435619984 582705611375616 168359623607186064 48658925715634520064 14062942737777746304144 4064228085576507141325824

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 286 5094 84670 1423686 24141022 410294310 6975432574 118586681478 2015992253086

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
 The isogeny class factors as 1.17.ag 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-2})$$$)$
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.a_ac $2$ (not in LMFDB) 2.17.m_cs $2$ (not in LMFDB) 2.17.g_t $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.17.a_ac $2$ (not in LMFDB) 2.17.m_cs $2$ (not in LMFDB) 2.17.g_t $3$ (not in LMFDB) 2.17.a_c $4$ (not in LMFDB) 2.17.ag_t $6$ (not in LMFDB) 2.17.ai_bg $8$ (not in LMFDB) 2.17.i_bg $8$ (not in LMFDB)