Properties

Label 2.191.aca_bor
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $( 1 - 27 x + 191 x^{2} )( 1 - 25 x + 191 x^{2} )$
Frobenius angles:  $\pm0.0686610702072$, $\pm0.140267993779$
Angle rank:  $2$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27555 1309496265 48512838773520 1771152658481831625 64615078566594932503875 2357221982375803598281416960 85993801863659954392502876769795 3137139829800460763960529859056671625 114445997957902045065261917529742477537680 4175104451057621730799081031727027952027871625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 140 35892 6962360 1330829828 254195021500 48551234713182 9273284398643860 1771197288530880388 338298681597872176040 64615048178312792561652

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.abb $\times$ 1.191.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 $\F_{191}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.191.ac_alh$2$(not in LMFDB)
2.191.c_alh$2$(not in LMFDB)
2.191.ca_bor$2$(not in LMFDB)