Properties

Label 2.199.abx_bly
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:  $( 1 - 28 x + 199 x^{2} )( 1 - 21 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.232771238785$
Angle rank:  $2$ (numerical)
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30788 1551345744 62088393230864 2459386043610949440 97393696153177682225948 3856886605653843552008714496 152736579889153104294058862670188 6048521402809360705014406645775381760 239527496488516009926580018392984547308944 9485528389592790069743128567871302916821882704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39173 7878640 1568246761 312079661221 62103833973326 12358664046460939 2459374186971386161 489415464057018508240 97393677359165392443053

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.av 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.ah_ahi$2$(not in LMFDB)
2.199.h_ahi$2$(not in LMFDB)
2.199.bx_bly$2$(not in LMFDB)
2.199.ak_gl$3$(not in LMFDB)
2.199.ae_bp$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ah_ahi$2$(not in LMFDB)
2.199.h_ahi$2$(not in LMFDB)
2.199.bx_bly$2$(not in LMFDB)
2.199.ak_gl$3$(not in LMFDB)
2.199.ae_bp$3$(not in LMFDB)
2.199.abm_bdb$6$(not in LMFDB)
2.199.abg_yf$6$(not in LMFDB)
2.199.e_bp$6$(not in LMFDB)
2.199.k_gl$6$(not in LMFDB)
2.199.bg_yf$6$(not in LMFDB)
2.199.bm_bdb$6$(not in LMFDB)