Properties

Label 1.389.g
Base Field $\F_{389}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{389}$
Dimension:  $1$
L-polynomial:  $1 + 6 x + 389 x^{2}$
Frobenius angles:  $\pm0.548605523983$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-95}) \)
Galois group:  $C_2$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 396 152064 58857084 22897797120 8907343648236 3464955145327104 1347867521613941724 524320466683995463680 203960661547055421793356 79340697341460740999176704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 396 152064 58857084 22897797120 8907343648236 3464955145327104 1347867521613941724 524320466683995463680 203960661547055421793356 79340697341460740999176704

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{389}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-95}) \).
All geometric endomorphisms are defined over $\F_{389}$.

Base change

This is a primitive isogeny class.

Twists

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