Properties

Label 2.193.abw_bkv
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:  $1 - 48 x + 957 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.106782388193$, $\pm0.213534342372$
Angle rank:  $2$ (numerical)
Number field:  4.0.624025.2
Galois group:  $D_{4}$
Jacobians:  72

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 72 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28895 1373061505 51678407454320 1925192198540640025 71709205251780376622375 2671085786981671266019467520 99495246507089463172416888036695 3706098385396083686009242177261250025 138048458700555530293691380877871047617520 5142167038127518809604972731240383918190312625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36860 7188482 1387537908 267786305906 51682555822430 9974730469423922 1925122953719239588 371548729914231256706 71708904873314513132300

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.624025.2.
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.bw_bkv$2$(not in LMFDB)