Properties

Label 1.227.m
Base Field $\F_{227}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{227}$
Dimension:  $1$
L-polynomial:  $1 + 12 x + 227 x^{2}$
Frobenius angles:  $\pm0.630376793357$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-191}) \)
Galois group:  $C_2$
Jacobians:  26

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 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 240 51840 11690640 2655244800 602740369200 136821732577920 31058537315390160 7050287997540403200 1600415374205723502960 363294289953413679427200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 240 51840 11690640 2655244800 602740369200 136821732577920 31058537315390160 7050287997540403200 1600415374205723502960 363294289953413679427200

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{227}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-191}) \).
All geometric endomorphisms are defined over $\F_{227}$.

Base change

This is a primitive isogeny class.

Twists

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