Properties

Label 1.401.at
Base Field $\F_{401}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{401}$
Dimension:  $1$
L-polynomial:  $1 - 19 x + 401 x^{2}$
Frobenius angles:  $\pm0.342662386815$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-1243}) \)
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
$A(\F_{q^r})$ 383 161243 64497200 25857088723 10368637602103 4157825155428800 1667287937434823863 668582463271142657763 268101567758470735194800 107508728670750601778397803

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 383 161243 64497200 25857088723 10368637602103 4157825155428800 1667287937434823863 668582463271142657763 268101567758470735194800 107508728670750601778397803

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{401}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1243}) \).
All geometric endomorphisms are defined over $\F_{401}$.

Base change

This is a primitive isogeny class.

Twists

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