Properties

Label 2.193.abx_blp
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 977 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0421729480035$, $\pm0.219099923147$
Angle rank:  $2$ (numerical)
Number field:  4.0.5745693.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28721 1370939493 51665281423217 1925129434993236549 71708951113082119874576 2671084885972362694611761061 99495243670743925502039459664593 3706098377432916337250006047460303493 138048458680673390548370024590979821973201 5142167038083922720329381730354984425266085888

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 145 36803 7186657 1387492675 267785356870 51682538388899 9974730185070817 1925122949582793475 371548729860719730097 71708904872706553920638

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.5745693.1.
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

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