Properties

Label 2.199.acd_bsk
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $( 1 - 28 x + 199 x^{2} )( 1 - 27 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.0936959350875$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 29756 1540051536 62034525741104 2459217132947674944 97393358188810034661476 3856886483314268838045378816 152736582268103828679132908092436 6048521415258264578822792358213137664 239527496528296194508977391087586307184304 9485528389683710389293460755493397556322698576

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 38885 7871800 1568139049 312078578275 62103832003406 12358664238953485 2459374192033203889 489415464138299521000 97393677360098926549325

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.abb 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.ab_anu$2$(not in LMFDB)
2.199.b_anu$2$(not in LMFDB)
2.199.cd_bsk$2$(not in LMFDB)
2.199.aq_dx$3$(not in LMFDB)
2.199.ak_acj$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ab_anu$2$(not in LMFDB)
2.199.b_anu$2$(not in LMFDB)
2.199.cd_bsk$2$(not in LMFDB)
2.199.aq_dx$3$(not in LMFDB)
2.199.ak_acj$3$(not in LMFDB)
2.199.abs_bgz$6$(not in LMFDB)
2.199.abm_bat$6$(not in LMFDB)
2.199.k_acj$6$(not in LMFDB)
2.199.q_dx$6$(not in LMFDB)
2.199.bm_bat$6$(not in LMFDB)
2.199.bs_bgz$6$(not in LMFDB)