Properties

Label 2.181.aby_blw
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 50 x + 984 x^{2} - 9050 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0363437804091$, $\pm0.167479033802$
Angle rank:  $2$ (numerical)
Number field:  4.0.247104.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24646 1055982516 35134859689414 1151909323634990544 37738602140474545196326 1236354265338605109419474196 40504199168232100009756212964966 1326958063319023661687364631379088384 43472473119580079586881407672896875781334 1424201691963302782365694629488911544546064276

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 132 32230 5925192 1073257654 194264272152 35161831001446 6364290952683012 1151936657546963614 208500535050463373172 37738596846591296171350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.247104.2.
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.by_blw$2$(not in LMFDB)