h.cond

强大的数学工具包

                               * * * * * * *
                               *   cond    *
                               * * * * * * *

        "conductor"
        SYNTAX: X = cond(E)

        E is an expression whose value is an elliptic curve over Q
        or a quadratic number field.

        If E is an elliptic curve over Q, X is assigned the conductor 
        of the global minimal model of E.
        Otherwise, X is assigned the norm of the conductor.
        In both cases, the factorization of the conductor is displayed.

        You can use nfon in order to compute the factorization of the
        conductor of an elliptic curve over Q over the quadratic number 
        field, specified by curnf. In this case X is assigned the norm.

        If the factorization is over Q, the factors and exponents are
        stored in AV (see "? avfunc"). If the conductor has its prime
        factorization over Q p1^e1 * ... * pN^eN in increasing order,
        then AV[0]=p1, AV[1]=e1, ..., AV[2*N-2]=pN, AV[2*N-1]=eN.
        
        For the representation of ideals in quadratic number fields,
        please see "?fact".


        Example 1: (correct)

                cond(EC(8, 9))


        Example 2: (correct)

                cond(EC(3^4, 3^6))


        Example 3: (correct)

                cond(EC(NF(A), NF(2*A-1))