Properties

Label 3.7.aj_bn_aen
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:  $1 - 9 x + 39 x^{2} - 117 x^{3} + 273 x^{4} - 441 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.0498744256324$, $\pm0.209638042653$, $\pm0.524777204314$
Angle rank:  $3$ (numerical)
Number field:  6.0.1305639.1
Galois group:  $A_4\times C_2$

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
$A(\F_{q^r})$ 89 108847 37405187 13339526391 4796042024159 1637863504126903 557473962960800576 191317740292278438471 65702998610871049393937 22538679394105663381021087

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 47 317 2315 16979 118331 821960 5756867 40347857 282466967

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 6.0.1305639.1.
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_bn_en$2$(not in LMFDB)