Complex multiplication

Elliptic curves have an endomorphism ring larger than the integers, which are higher dimensions of abelian varieties.

C/ΘZ[i]

C is complex multiplication, and Z[i] is the Gaussian integer ring, and θ is any non-zero complex number.

You can see always the Gaussian integer as module in Elliptic curves.

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Y^2=X^3-X+1

59 is the Gaussian prime.

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The Gaussian prime must be symmetry in any Elliptic curves.

2=(1-i)(1+i)=(-1-i)(-1+i)

This is the norm. 1±i,-1±i are Gaussian primes.

±3,±3i,5=(2-i)(2+i)=(1-2i)(1+2i),±7,±7i,13=(2+3i)(2-3i)=(3+2i)(3-2i),17=(4-i)(4+i)=(1+4i)(1-4i)

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Y^2=4X^3-X

59 is the Gaussian prime.

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I think that it is fractal.