Properties

Label 3.7.aj_bq_afd
Base Field $\F_{7}$
Dimension $3$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{7}$
Dimension:  $3$
L-polynomial:  $1 - 9 x + 42 x^{2} - 133 x^{3} + 294 x^{4} - 441 x^{5} + 343 x^{6}$
Frobenius angles:  $\pm0.0337411547966$, $\pm0.282571984656$, $\pm0.476016355688$
Angle rank:  $3$ (numerical)
Number field:  6.0.1714608.1
Galois group:  $D_{6}$

This isogeny class is simple and geometrically simple.

Newton polygon

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

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
$A(\F_{q^r})$ 97 122511 41003452 13303346979 4678048479367 1623844456271856 557031695003568049 191235483740749262763 65690218868207530794148 22542275480741043427678431

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 53 350 2309 16559 117320 821309 5754389 40340006 282512033

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7}$
The endomorphism algebra of this simple isogeny class is 6.0.1714608.1.
All geometric endomorphisms are defined over $\F_{7}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.j_bq_fd$2$(not in LMFDB)
3.7.d_a_ah$3$(not in LMFDB)
3.7.g_v_ce$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.7.j_bq_fd$2$(not in LMFDB)
3.7.d_a_ah$3$(not in LMFDB)
3.7.g_v_ce$3$(not in LMFDB)
3.7.ag_v_ace$6$(not in LMFDB)
3.7.ad_a_h$6$(not in LMFDB)