Properties

Label 3.7.aj_bq_afc
Base Field $\F_{7}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $1 - 9 x + 42 x^{2} - 132 x^{3} + 294 x^{4} - 441 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.0750503069484$, $\pm0.268018317244$, $\pm0.480080482251$
Angle rank:  $3$ (numerical)
Number field:  6.0.256065624.1
Galois group:  $S_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 98 123676 41478794 13508387424 4732912055648 1632626817855292 558027883801579394 191347369566177976704 65706517812209444621738 22544852863465723504086016

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 53 353 2345 16754 117953 822779 5757761 40350017 282544328

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 6.0.256065624.1.
All geometric endomorphisms are defined over $\F_{7}$.

Base change

This is a primitive isogeny class.

Twists

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