Properties

Label 1.283.az
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:  $1 - 25 x + 283 x^{2}$
Frobenius angles:  $\pm0.233379450635$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}) \)
Galois group:  $C_2$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 259 80031 22670788 6414404619 1815234494269 513710715715344 145380128282952703 41142576380327368275 11643349118745789552604 3295067800661307805392111

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 259 80031 22670788 6414404619 1815234494269 513710715715344 145380128282952703 41142576380327368275 11643349118745789552604 3295067800661307805392111

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{283}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \).
All geometric endomorphisms are defined over $\F_{283}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
1.283.z$2$(not in LMFDB)
1.283.ah$3$(not in LMFDB)
1.283.bg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.283.z$2$(not in LMFDB)
1.283.ah$3$(not in LMFDB)
1.283.bg$3$(not in LMFDB)
1.283.abg$6$(not in LMFDB)
1.283.h$6$(not in LMFDB)