sage: T.<t1,t2,u1,u2> = QQ[]
sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1-
u2)^2 -1])
sage: TJ.genus()
4294967295
sage: TJ.dimension()
1

I'm very skeptical about that answer (I realize that Singular is doing
the calculation) especially since (for example).  Even if it's
calculating arithmetic genus I can't imagine that that curve could
have that many singularities.

sage: TK = Ideal([t1^2/4 + u1^2 - 1,t2^2/4 + u2^2 - 1, (t1-t2)^2 + (u1-
u2)^2 -1])
sage: TK.genus()
3
sage: TK.dimension()
1

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