Properties

 Label 2.256.acd_bwb Base Field $\F_{2^{8}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

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Invariants

 Base field: $\F_{2^{8}}$ Dimension: $2$ L-polynomial: $1 - 55 x + 1249 x^{2} - 14080 x^{3} + 65536 x^{4}$ Frobenius angles: $\pm0.0267010353124$, $\pm0.243100561557$ Angle rank: $2$ (numerical) Number field: 4.0.20876009.1 Galois group: $D_{4}$

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 a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 52651 4260571571 281432521031104 18446773344930660899 1208925510898320008823451 79228155465572346498856752896 5192296803422887482161809341609691 340282366640762300689315650529640367299 22300745197518732076376248135644482776982464 1461501637328554473181830681726676088040334231251

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 202 65010 16774687 4294974114 1099511347002 281474951668671 72057593273096122 18446744058521171394 4722366482655368945887 1208925819612686586514450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
 The endomorphism algebra of this simple isogeny class is 4.0.20876009.1.
All geometric endomorphisms are defined over $\F_{2^{8}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.256.cd_bwb $2$ (not in LMFDB)