Properties

Label 2.193.acb_bpv
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:  $1 - 53 x + 1087 x^{2} - 10229 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0349017074441$, $\pm0.133355644639$
Angle rank:  $2$ (numerical)
Number field:  4.0.29525.1
Galois group:  $D_{4}$
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28055 1364006045 51634173782255 1925040206770379525 71708807001085748982000 2671085010981832301789550005 99495245591806833319248260306855 3706098385664899566889491122526791525 138048458703918206577008865846543373406855 5142167038126605789286621858128165465899808000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 141 36615 7182327 1387428363 267784818706 51682540807695 9974730377663787 1925122953858875283 371548729923281688081 71708904873301780817950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.29525.1.
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.cb_bpv$2$(not in LMFDB)