Properties

Label 2.256.acj_cdk
Base Field $\F_{2^{8}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x )^{2}( 1 - 29 x + 256 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.138932406859$
Angle rank:  $1$ (numerical)

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
$A(\F_{q^r})$ 51300 4240150200 281302071277500 18446279187751786800 1208924837639368840732500 79228161252780618124711665000 5192296858390826076353332372406700 340282366911323013946937837899494607200 22300745198339959529685902048275641048802500 1461501637329150291523852651298084571015305055000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 196 64696 16766908 4294859056 1099510734676 281474972228968 72057594035929516 18446744073188297056 4722366482829270623428 1208925819613179435895576

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The isogeny class factors as 1.256.abg $\times$ 1.256.abd 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 $\F_{2^{8}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.256.ad_aqa$2$(not in LMFDB)
2.256.d_aqa$2$(not in LMFDB)
2.256.cj_cdk$2$(not in LMFDB)
2.256.an_bw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.256.ad_aqa$2$(not in LMFDB)
2.256.d_aqa$2$(not in LMFDB)
2.256.cj_cdk$2$(not in LMFDB)
2.256.an_bw$3$(not in LMFDB)
2.256.abd_ts$4$(not in LMFDB)
2.256.bd_ts$4$(not in LMFDB)
2.256.abt_blo$6$(not in LMFDB)
2.256.n_bw$6$(not in LMFDB)
2.256.bt_blo$6$(not in LMFDB)