Properties

Label 1.277.ag
Base Field $\F_{277}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{277}$
Dimension:  $1$
L-polynomial:  $1 - 6 x + 277 x^{2}$
Frobenius angles:  $\pm0.442308503721$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-67}) \)
Galois group:  $C_2$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 272 77248 21258704 5887224576 1630791014672 451729687723456 125129118702705872 34660765692134673408 9601032096918898869008 2659485890899939166968768

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 272 77248 21258704 5887224576 1630791014672 451729687723456 125129118702705872 34660765692134673408 9601032096918898869008 2659485890899939166968768

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{277}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-67}) \).
All geometric endomorphisms are defined over $\F_{277}$.

Base change

This is a primitive isogeny class.

Twists

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