Properties

Label 2.64.abf_oe
Base Field $\F_{2^{6}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2^{6}}$
Dimension:  $2$
L-polynomial:  $( 1 - 8 x )^{2}( 1 - 15 x + 64 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.113134082257$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 2450 15876000 68322309650 281317163400000 1152865552114267250 4722349644870882444000 19342809311458203331120850 79228162097374332559280400000 324518553650518532056123744800050 1329227995577124107633773961178900000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 34 3872 260626 16767808 1073689714 68719231712 4398045646546 281474975229568 18014398509042994 1152921504426616352

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.aq $\times$ 1.64.ap and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{6}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.ab_aei$2$(not in LMFDB)
2.64.b_aei$2$(not in LMFDB)
2.64.bf_oe$2$(not in LMFDB)
2.64.ah_i$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.ab_aei$2$(not in LMFDB)
2.64.b_aei$2$(not in LMFDB)
2.64.bf_oe$2$(not in LMFDB)
2.64.ah_i$3$(not in LMFDB)
2.64.ap_ey$4$(not in LMFDB)
2.64.p_ey$4$(not in LMFDB)
2.64.ax_jo$6$(not in LMFDB)
2.64.h_i$6$(not in LMFDB)
2.64.x_jo$6$(not in LMFDB)