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nLab > Latest Changes: elliptic curve

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 8th 2014
    • (edited Apr 8th 2014)

    added a chunk of some standard basics to elliptic curve – Definition over a general ring.

    Also touched/briefly created various related entries, such as Weierstrass equation, Weierstrass elliptic function, cubic curve, j-invariant etc.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 3rd 2015

    I did a little touch-up at Weierstrass elliptic curve. Particularly, the prior version said that ℘\wp parametrized a complex torus, whereas I think it is more accurate to say we have a map

    (℘,℘′):ℂ/L→cubic(\wp, \wp'): \mathbb{C}/L \to cubic

    so that it is the torus that is parametrizing the cubic (rather than the thing that is being parametrized).

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 3rd 2015

    True, thanks.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2020

    added pointer to:

    diff, v36, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2020
    • (edited Nov 16th 2020)

    added pointer to:

    diff, v37, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 22nd 2021

    Not so important, but I just noticed that the rendering of the elliptic group law on the nLab page here comes out strange: the first square root symbol over-extends downwards so much that it looks weird.

    In contrast, here on the nForum it displays as expected:

    f(x,y)=x1−2δy 2+εy 4+y1−2δx 2+εx 41−εx 2y 2 f(x,y) \;=\; \frac{ x \sqrt{1- 2 \delta y^2 + \epsilon y^4} + y \sqrt{1- 2 \delta x^2 + \epsilon x^4} } {1- \epsilon x^2 y^2}

  7. Linking to the new page torsion points of an elliptic curve. Also changing the naming of the section where the formal group law is described to ’Formal group law’ rather than ’Group law’, the latter being commonly used to refer to the actual group structure of an elliptic curve.

    diff, v41, current

  8. Update reference to Sutherland’s lecture notes.

    Anonymous

    diff, v42, current

  9. Improved typesetting.

    Joseph Martin

    diff, v44, current

1 to 9 of 9

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