Properties

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

Learn more about

Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 921 x^{2} - 8977 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0606665304000$, $\pm0.244825545542$
Angle rank:  $2$ (numerical)
Number field:  4.0.28463597.1
Galois group:  $D_{4}$
Jacobians:  21

This isogeny class is simple and geometrically 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 21 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28379 1317551833 48545002152881 1771223956304745293 64615095058595342610544 2357221358098397349537868513 85993798659107465070202710333869 3137139819809980869896557873359300437 114445997936749219306220546609723326061039 4175104451035046587228462112839862126342295808

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36115 6966979 1330883403 254195086380 48551221855063 9273284053075621 1771197282890356899 338298681535345104811 64615048177963413520590

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.28463597.1.
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.bv_bjl$2$(not in LMFDB)