Properties

Label 3.7.aj_bm_aei
Base Field $\F_{7}$
Dimension $3$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $1 - 9 x + 38 x^{2} - 112 x^{3} + 266 x^{4} - 441 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.0283467889665$, $\pm0.193732293337$, $\pm0.536888824784$
Angle rank:  $3$ (numerical)
Number field:  6.0.30088184.1
Galois group:  $S_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 86 104060 36096350 13240594400 4794339367136 1635819081825500 557193261508696262 191339982259009865600 65701512455397896151950 22536096965623129594956800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 45 305 2297 16974 118185 821547 5757537 40346945 282434600

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 6.0.30088184.1.
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_bm_ei$2$(not in LMFDB)