Properties

Label 2.199.abw_bkw
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:  $( 1 - 28 x + 199 x^{2} )( 1 - 20 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.249200223051$
Angle rank:  $2$ (numerical)
Jacobians:  90

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 90 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30960 1552953600 62093622472560 2459388936883507200 97393642291828872658800 3856886308088067056375865600 152736579067150039017126835568880 6048521402099003438196377948155084800 239527496493560034455534281942260928654320 9485528389622582293594773478217100542574240000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 152 39214 7879304 1568248606 312079488632 62103829181902 12358663979948648 2459374186682549566 489415464067324730456 97393677359471287288174

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.au 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 $\F_{199}$.

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.ai_agg$2$(not in LMFDB)
2.199.i_agg$2$(not in LMFDB)
2.199.bw_bkw$2$(not in LMFDB)
2.199.aj_gw$3$(not in LMFDB)
2.199.ad_cg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ai_agg$2$(not in LMFDB)
2.199.i_agg$2$(not in LMFDB)
2.199.bw_bkw$2$(not in LMFDB)
2.199.aj_gw$3$(not in LMFDB)
2.199.ad_cg$3$(not in LMFDB)
2.199.abl_bck$6$(not in LMFDB)
2.199.abf_xu$6$(not in LMFDB)
2.199.d_cg$6$(not in LMFDB)
2.199.j_gw$6$(not in LMFDB)
2.199.bf_xu$6$(not in LMFDB)
2.199.bl_bck$6$(not in LMFDB)