Properties

Label 2.191.abx_blq
Base field $\F_{191}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 978 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0892328849414$, $\pm0.198490921895$
Angle rank:  $2$ (numerical)
Number field:  4.0.1100801.1
Galois group:  $D_{4}$
Jacobians:  $24$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $28052$ $1314741136$ $48537577688912$ $1771232558340531776$ $64615261280224090136812$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $143$ $36037$ $6965912$ $1330889865$ $254195740293$ $48551239321822$ $9273284357131091$ $1771197286583072049$ $338298681560731593032$ $64615048177850266351677$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{191}$.

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.1100801.1.

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.bx_blq$2$(not in LMFDB)