Properties

Label 2.199.aca_bpe
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:  $( 1 - 28 x + 199 x^{2} )( 1 - 24 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.176204172288$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30272 1546051584 62066562721856 2459339257276661760 97393717264364738879552 3856887256387699843057115136 152736583017145246244570841906752 6048521411971823893833414240255344640 239527496503445372583055033203519819407936 9485528389579530111133538380671197505602248704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 148 39038 7875868 1568216926 312079728868 62103844451486 12358664299562092 2459374190696912446 489415464087522985012 97393677359029244399678

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.ay 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.ae_ako$2$(not in LMFDB)
2.199.e_ako$2$(not in LMFDB)
2.199.ca_bpe$2$(not in LMFDB)
2.199.an_fe$3$(not in LMFDB)
2.199.ah_ak$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ae_ako$2$(not in LMFDB)
2.199.e_ako$2$(not in LMFDB)
2.199.ca_bpe$2$(not in LMFDB)
2.199.an_fe$3$(not in LMFDB)
2.199.ah_ak$3$(not in LMFDB)
2.199.abp_bfa$6$(not in LMFDB)
2.199.abj_zm$6$(not in LMFDB)
2.199.h_ak$6$(not in LMFDB)
2.199.n_fe$6$(not in LMFDB)
2.199.bj_zm$6$(not in LMFDB)
2.199.bp_bfa$6$(not in LMFDB)