Properties

Label 2.199.aca_bph
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:  $( 1 - 27 x + 199 x^{2} )( 1 - 25 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0936959350875$, $\pm0.153403448314$
Angle rank:  $2$ (numerical)
Jacobians:  15

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 15 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30275 1546295625 62070255976400 2459369981558975625 97393902266009290893875 3856888155503483602296480000 152736586731691134556253029655075 6048521425354997856439716269132255625 239527496545898703464486168504741421630800 9485528389697488101927268042493993509095515625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 148 39044 7876336 1568236516 312080321668 62103858929102 12358664600124172 2459374196138611396 489415464174265914064 97393677360240390687524

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abb $\times$ 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ac_akr$2$(not in LMFDB)
2.199.c_akr$2$(not in LMFDB)
2.199.ca_bph$2$(not in LMFDB)