Properties

Label 2.191.abw_bkt
Base Field $\F_{191}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 955 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.118978615897$, $\pm0.201829070985$
Angle rank:  $2$ (numerical)
Number field:  4.0.3933072.3
Galois group:  $D_{4}$
Jacobians:  28

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28221 1316594313 48547222774164 1771269796080712377 64615379677307392334181 2357222527085358974473076112 85993802217701159641360138498389 3137139827700994644239153772302657193 114445997946651005362025092478547913675284 4175104451023946405551245002077413562637670873

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36088 6967296 1330917844 254196206064 48551245932454 9273284436822480 1771197287345543140 338298681564614465280 64615048177791624100168

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.3933072.3.
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.bw_bkt$2$(not in LMFDB)