Category : BASIC Source Code
Archive   : UBAS830.ZIP
Filename : ECMJAC.UB

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Lenstra Elliptic Curve Method
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programed by Hiromi Suyama, 21 Nov. 1988
טl written in UBASIC86 version 6.20 (produced by Y.Kida for Multiple- Precision Arithmetic & Number Theory)
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ó2˜ˆReferences
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<˜[ [1]D.V.Chudnovsky and G.V.Chudnovsky, Sequences of numbers generated by addition in formal groups and new primality and factorization tests, Advances in Applied Math. 7(1986),385-434.
7F˜Ì [2]H.W.Lenstra,Jr., Factoring integers with elliptic curves, Ann. of Math. 126(1987),649-673.
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[3]P.L.Montgomery, Speeding the Pollard and Elliptic Curve Methods of factorization, Math. Comp. 48(1987),243-264.
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[4]T.Ono, On the relative Mordell-Weil rank of elliptic quartic curves, J. Math. Soc. Japan 32(1980),665-670.
Èd˜][5]Section 4.6.3(Evaluation of Powers) in D.E.Knuth, The Art of Computer Programming, Vol.2, second ed., Addison-Wesley, 1981.
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˜¢ The parametrization of elliptic curves ' ' E(KK)={(S:T:C:D) : S^2+C^2=T^2 , KK*S^2+D^2=T^2}-{(0:0:0:0)}
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