Properties

Label 3.11.ao_ds_apj
Base Field $\F_{11}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
Weil polynomial:  $1 - 14 x + 96 x^{2} - 399 x^{3} + 1056 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.109163587838$, $\pm0.259064841799$, $\pm0.339864730746$
Angle rank:  $3$ (numerical)
Number field:  6.0.9380707.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 377 1730807 2523532817 3202652387467 4180557855040307 5554119060208014647 7398687153153882015625 9850516361083237324765267 13110791588866530003071162432 17449738766075509910920927334207

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 118 1423 14938 161178 1769713 19483056 214375938 2358091108 25937924778

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.