Properties

Label 1.83.c
Base field $\F_{83}$
Dimension $1$
$p$-rank $1$
Ordinary Yes
Supersingular No
Simple Yes
Geometrically simple Yes
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{83}$
Dimension:  $1$
L-polynomial:  $1 + 2 x + 83 x^{2}$
Frobenius angles:  $\pm0.535009590967$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-82}) \)
Galois group:  $C_2$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 86 7052 571298 47445856 3939106246 326941276844 27136043737714 2252292171654528 186940255990418294 15516041190780312332

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 86 7052 571298 47445856 3939106246 326941276844 27136043737714 2252292171654528 186940255990418294 15516041190780312332

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-82}) \).
All geometric endomorphisms are defined over $\F_{83}$.

Base change

This is a primitive isogeny class.

Twists

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