Properties

Label 1.283.abh
Base Field $\F_{283}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{283}$
Dimension:  $1$
L-polynomial:  $1 - 33 x + 283 x^{2}$
Frobenius angles:  $\pm0.0624381128342$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-43}) \)
Galois group:  $C_2$
Jacobians:  1

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 251 79567 22657268 6414134571 1815230662421 513710684348944 145380128444037479 41142576392032868883 11643349118992680449324 3295067800664501275179007

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 251 79567 22657268 6414134571 1815230662421 513710684348944 145380128444037479 41142576392032868883 11643349118992680449324 3295067800664501275179007

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{283}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-43}) \).
All geometric endomorphisms are defined over $\F_{283}$.

Base change

This is a primitive isogeny class.

Twists

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