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- W2964152072 abstract "If an integer n is written as a sum of two biquadrates intwo different ways, then the elliptic curve y2 = x3 − nx has positiverank. We utilize Euler’s parametrization to introduce some homoge-neous equations to prove that En has rank ≥ 3. If moreover n is oddand the parity conjecture is true, then the curve has even rank ≥ 4.Finally, some examples of ranks equal to 4, 5, 6, 7, 8 and 10, are alsoobtained." @default.
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- W2964152072 date "2014-01-01" @default.
- W2964152072 modified "2023-09-24" @default.
- W2964152072 title "SUMS OF TWO BIQUADRATES AND ELLIPTIC CURVES OF RANK ≥ 4" @default.
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