Properties

Label 2.64.abb_lt
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $1 - 27 x + 305 x^{2} - 1728 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0514697705289$, $\pm0.252940519903$
Angle rank:  $2$ (numerical)
Number field:  4.0.381465.2
Galois group:  $D_{4}$
Jacobians:  6

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2647 16297579 68676859696 281502622378035 1152920316123871327 4722344125408811778496 19342791415281174698884447 79228150510452107316694554915 324518549977449280451259986520496 1329227996127591587083172495640770779

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3978 261983 16778866 1073740718 68719151391 4398041577422 281474934064546 18014398305146687 1152921504904070778

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.381465.2.
All geometric endomorphisms are defined over $\F_{2^{6}}$.

Base change

This is a primitive isogeny class.

Twists

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