It is often asserted that the $j$-invariant was first introduced by Felix Klein. Is there any evidence for this claim? What works of Felix Klein do deal with it? What is the origin of the symbol $j$ used for it? Where it had first appeared?


Felix Klein, Über die Transformation der elliptischen Funktionen und die Auflösung der Gleichungen fünften Grades, Math. Ann. 14,‎ 111-172 (1878-1879).

There is also a slightly earlier brief note in Italian, Sull' equazioni dell' Icosaedro nella risoluzione delle equazioni del quinto grado, Rendiconti Reale Istituto Lombardo, Serie 2, vol. 10, p. 253-255‎ (1877).

Dedekind may have gotten there first, see Dedekind or Klein (p. 67).

Notation: Klein used capital $J$, there is a factor 1728 difference with the $j$-invariant. (Read more about the origin of this factor.)

  • 1
    $\begingroup$ And other sources suggest Hermite (around 1850) or even Gauss... hsm.stackexchange.com/questions/7628/… surely it must be in one of Euler's collected works (...JK). $\endgroup$ – SWS Apr 26 '19 at 15:49

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