Properties

Label 2.199.acc_bri
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:  $( 1 - 28 x + 199 x^{2} )( 1 - 26 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.126927281034$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 29928 1542129984 62046417540744 2459267748751656960 97393535783741510069448 3856887010152228461786185536 152736583556598983041184406574248 6048521417515945877455928005581373440 239527496528739361782742956437691674685864 9485528389664414164494146947187207664835408704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 38938 7873310 1568171326 312079147346 62103840486586 12358664343211934 2459374192951194046 489415464139205024210 97393677359900800497178

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.aba 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.ac_ams$2$(not in LMFDB)
2.199.c_ams$2$(not in LMFDB)
2.199.cc_bri$2$(not in LMFDB)
2.199.ap_ei$3$(not in LMFDB)
2.199.aj_abs$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ac_ams$2$(not in LMFDB)
2.199.c_ams$2$(not in LMFDB)
2.199.cc_bri$2$(not in LMFDB)
2.199.ap_ei$3$(not in LMFDB)
2.199.aj_abs$3$(not in LMFDB)
2.199.abr_bgi$6$(not in LMFDB)
2.199.abl_bai$6$(not in LMFDB)
2.199.j_abs$6$(not in LMFDB)
2.199.p_ei$6$(not in LMFDB)
2.199.bl_bai$6$(not in LMFDB)
2.199.br_bgi$6$(not in LMFDB)