Properties

Label 2.64.abe_np
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:  $( 1 - 15 x + 64 x^{2} )^{2}$
Frobenius angles:  $\pm0.113134082257$, $\pm0.113134082257$
Angle rank:  $1$ (numerical)
Jacobians:  3

This isogeny class is not 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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2500 16000000 68460722500 281434176000000 1152950336902562500 4722404864699536000000 19342842402600710328722500 79228180569952877158656000000 324518563314017073918940214402500 1329228000321092509518790810000000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 35 3903 261155 16774783 1073768675 68720035263 4398053170595 281475040857343 18014399045474915 1152921508541353023

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{6}}$
The isogeny class factors as 1.64.ap 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-31}) \)$)$
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.a_adt$2$(not in LMFDB)
2.64.be_np$2$(not in LMFDB)
2.64.p_gf$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.64.a_adt$2$(not in LMFDB)
2.64.be_np$2$(not in LMFDB)
2.64.p_gf$3$(not in LMFDB)
2.64.a_dt$4$(not in LMFDB)
2.64.ap_gf$6$(not in LMFDB)