Properties

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

Learn more about

Invariants

Base field:  $\F_{17}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 17 x^{2} )^{2}$
Frobenius angles:  $\pm0.177280642489$, $\pm0.177280642489$
Angle rank:  $1$ (numerical)
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 121 75625 24285184 7035015625 2022342812281 583087267840000 168401996374543129 48661783896050015625 14063036162888693026816 4064222751691998577515625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 260 4942 84228 1424324 24156830 410397572 6975842308 118587469294 2015989607300

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{17}$
The isogeny class factors as 1.17.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$
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_ap$2$(not in LMFDB)
2.17.o_df$2$(not in LMFDB)
2.17.h_bg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.17.a_ap$2$(not in LMFDB)
2.17.o_df$2$(not in LMFDB)
2.17.h_bg$3$(not in LMFDB)
2.17.a_p$4$(not in LMFDB)
2.17.ah_bg$6$(not in LMFDB)