Properties

Label 2.199.acb_bqg
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:  $( 1 - 28 x + 199 x^{2} )( 1 - 25 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.153403448314$
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
$A(\F_{q^r})$ 30100 1544130000 62057080783600 2459308136954760000 97393652036485928315500 3856887241732189873464480000 152736583649918378454709992010300 6048521415641616953236583650647840000 239527496517145922027450138582368249529200 9485528389617622154801112071143558223573250000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 38989 7874664 1568197081 312079519857 62103844215502 12358664350762863 2459374192189077841 489415464115516684536 97393677359420358532549

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.az 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.ad_alq$2$(not in LMFDB)
2.199.d_alq$2$(not in LMFDB)
2.199.cb_bqg$2$(not in LMFDB)
2.199.ao_et$3$(not in LMFDB)
2.199.ai_abb$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ad_alq$2$(not in LMFDB)
2.199.d_alq$2$(not in LMFDB)
2.199.cb_bqg$2$(not in LMFDB)
2.199.ao_et$3$(not in LMFDB)
2.199.ai_abb$3$(not in LMFDB)
2.199.abq_bfr$6$(not in LMFDB)
2.199.abk_zx$6$(not in LMFDB)
2.199.i_abb$6$(not in LMFDB)
2.199.o_et$6$(not in LMFDB)
2.199.bk_zx$6$(not in LMFDB)
2.199.bq_bfr$6$(not in LMFDB)