Properties

Label 3.11.ao_dp_aor
Base Field $\F_{11}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
L-polynomial:  $1 - 14 x + 93 x^{2} - 381 x^{3} + 1023 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0701462554279$, $\pm0.192008360592$, $\pm0.399253926210$
Angle rank:  $3$ (numerical)
Number field:  6.0.62037703.1
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
$A(\F_{q^r})$ 359 1628783 2392406156 3128776499407 4167652624327664 5562592194686635472 7404414418494749999401 9850940839839779776909423 13109700078781101300038026556 17449103909118474912829997796608

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 112 1351 14596 160683 1772413 19498134 214385172 2357894791 25936981107

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 6.0.62037703.1.
All geometric endomorphisms are defined over $\F_{11}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.11.o_dp_or$2$(not in LMFDB)