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In number theory, Szpiro's conjecture concerns a relationship between the conductor and the discriminant of an elliptic curve. In a general form, it is equivalent to the well-known abc conjecture. It is named for Lucien Szpiro who formulated it in the 1980s. The conjecture states that: given ε > 0, there exists a constant ''C''(ε) such that for any elliptic curve ''E'' defined over Q with minimal discriminant Δ and conductor ''f'', we have : The modified Szpiro conjecture states that: given ε > 0, there exists a constant ''C''(ε) such that for any elliptic curve ''E'' defined over Q with invariants ''c''4, ''c''6 and conductor ''f'' (see Tate's algorithm#Notation), we have : ==References== * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Szpiro's conjecture」の詳細全文を読む スポンサード リンク
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