Properties

Label 2.64.ay_kb
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:  $1 - 24 x + 261 x^{2} - 1536 x^{3} + 4096 x^{4}$
Frobenius angles:  $\pm0.0933668599286$, $\pm0.317397908986$
Angle rank:  $2$ (numerical)
Number field:  4.0.7482640.2
Galois group:  $D_{4}$
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2798 16558564 68813712614 281512808906560 1152895195905212798 4722338840823080851396 19342807524904650133351478 79228170287774628819396445440 324518562251301393890762378184974 1329228000322405894622907319507149604

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 41 4043 262505 16779471 1073717321 68719074491 4398045240329 281475004327711 18014398986482345 1152921508542492203

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The endomorphism algebra of this simple isogeny class is 4.0.7482640.2.
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.y_kb$2$(not in LMFDB)