Properties

Label 2.199.aby_bnj
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 199 x^{2} )^{2}$
Frobenius angles:  $\pm0.153403448314$, $\pm0.153403448314$
Angle rank:  $1$ (numerical)
Jacobians:  47

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 47 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30625 1550390625 62092824010000 2459460991222265625 97394196115326732015625 3856888913921733456900000000 152736588113505724714099978875625 6048521425738350231493433654253515625 239527496534748430982139499548146308090000 9485528389631399867434823365104451554931640625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 150 39148 7879200 1568294548 312081263250 62103871141198 12358664711933550 2459374196294485348 489415464151483077600 97393677359561822670748

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$
All geometric endomorphisms are defined over $\F_{199}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.a_ait$2$(not in LMFDB)
2.199.by_bnj$2$(not in LMFDB)
2.199.z_qk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.a_ait$2$(not in LMFDB)
2.199.by_bnj$2$(not in LMFDB)
2.199.z_qk$3$(not in LMFDB)
2.199.a_it$4$(not in LMFDB)
2.199.az_qk$6$(not in LMFDB)