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In this very short note, we show that there is a relation between the leading term at $s=1$ of an $L$-function of an elliptic curve defined over an number field and the term that follows.

publications mathématiques de l'université de franche-comté besançon. algèbre et théorie des nombres/publications mathématiques de besançon. algèbre et théorie des nombres

The sub-leading coefficient of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>L</mml:mi></mml:math>-function of an elliptic curve

The sub-leading coefficient of the L-function of an elliptic curve