Properties

Label 3.11.an_cy_alf
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:  $1 - 13 x + 76 x^{2} - 291 x^{3} + 836 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0354721676546$, $\pm0.103262097857$, $\pm0.494210615205$
Angle rank:  $3$ (numerical)
Number field:  6.0.2343728.1
Galois group:  $S_4\times C_2$

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
$A(\F_{q^r})$ 367 1512407 2178396028 3027725383475 4158835374916837 5564732250376667888 7400452781633010860183 9848705743351045280314475 13110142522400296216941219508 17449735445916943529157064457567

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 105 1226 14117 160339 1773096 19487705 214336533 2357974370 25937919845

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.