Properties

Label 1.443.at
Base Field $\F_{443}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{443}$
Dimension:  $1$
L-polynomial:  $1 - 19 x + 443 x^{2}$
Frobenius angles:  $\pm0.350939526990$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-1411}) \)
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
$A(\F_{q^r})$ 425 196775 86956700 38513786875 17061549883375 7558269059637200 3348313265745927925 1483302777009295381875 657103130188470285685700 291096686672860287512546375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 425 196775 86956700 38513786875 17061549883375 7558269059637200 3348313265745927925 1483302777009295381875 657103130188470285685700 291096686672860287512546375

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{443}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1411}) \).
All geometric endomorphisms are defined over $\F_{443}$.

Base change

This is a primitive isogeny class.

Twists

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