Properties

Label 2.199.abx_bmi
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:  $( 1 - 26 x + 199 x^{2} )( 1 - 23 x + 199 x^{2} )$
Frobenius angles:  $\pm0.126927281034$, $\pm0.196619630811$
Angle rank:  $2$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30798 1552157604 62099991653544 2459474497819712160 97394168674300405771098 3856888560860574883797231936 152736586386810577825410738934938 6048521420029713448659036837706803840 239527496522186117495283705500825185877064 9485528389624232532353831810951367976709609604

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39193 7880110 1568303161 312081175321 62103865456186 12358664572218199 2459374193973310801 489415464125815083010 97393677359488231291153

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.aba $\times$ 1.199.ax 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ad_ahs$2$(not in LMFDB)
2.199.d_ahs$2$(not in LMFDB)
2.199.bx_bmi$2$(not in LMFDB)