Properties

Label 3.7.aj_bp_aex
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:  $1 - 9 x + 41 x^{2} - 127 x^{3} + 287 x^{4} - 441 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.0694611744153$, $\pm0.246479041091$, $\pm0.496921726293$
Angle rank:  $3$ (numerical)
Number field:  6.0.244361927.1
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
$A(\F_{q^r})$ 95 118655 40094465 13472681975 4765238252225 1636097906252735 557777384517009920 191291127247769841575 65702482696227733419695 22543253749683243072523775

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 51 341 2339 16869 118203 822408 5756067 40347539 282524291

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 6.0.244361927.1.
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_bp_ex$2$(not in LMFDB)