Properties

Label 2.191.aby_bmn
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:  $1 - 50 x + 1001 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0374478905433$, $\pm0.196270118167$
Angle rank:  $2$ (numerical)
Number field:  4.0.1548864.3
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27883 1312815289 48526845453700 1771186533895958329 64615090818737263808803 2357221631621080503528490000 85993799664567566258665229091763 3137139820894955797008388510173407529 114445997929606947933349048322420890015300 4175104450984315085760007594810479449840804809

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35984 6964372 1330855284 254195069702 48551227488758 9273284161501082 1771197283502922724 338298681514232780812 64615048177178279052704

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.1548864.3.
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.by_bmn$2$(not in LMFDB)