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Tables of Elliptic Curves over Number Fields: Notation

Tables of Elliptic Curves over Number Fields: Notation


The tables list curves over a number field K.  This field is an extension of the rational numbers Q found by adjoining to Q a root of the polynomial listed as f .  We let a be a root of this polynomial, so that K=Q(a). Quantities in the tables will be given as linear combinations of the power basis (1, a, ..., an-1) for K.

Each lines is listed as:

N      [A, B]      [n1, n2]      n1*n2      J      C

where:
  • N is the norm of the conductor;
  • A and B are the coefficients in y2 = x3 + Ax + B;
  • The torsion subgroup is given by Z/n1+Z/n2 has order n1*n2;
  • J is the j-invariant of the curve;
  • C is the actual conductor, given as a principal ideal.