Properties

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

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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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)