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  "body": "\n## Summary\n\nThe image of J is the image of the stable [[J-homomorphism|YYJPRD1HYW]] $J \\colon \\pi_r(SO) \\to \\pi_r^s$ inside the [[stable homotopy groups of spheres|HGZAYPQBXW]].\nIt is the part of the stable stems that comes from rotations, and it is known completely.\nIn degree $4k - 1$ it is cyclic of order equal to the denominator of $B_{2k}/4k$, where $B_{2k}$ is a [[Bernoulli number|0KC00K7KY4]].\nIt is the most regular and best understood part of the stable homotopy groups of spheres.\n\n## Explanations\n\n### L1 human\n\nThe stable homotopy groups of spheres look chaotic, but a part of them follows a clear rule.\nThat part comes from twisting spheres by rotations, and it is called the image of J.\nIts sizes are given by Bernoulli numbers.\nFor instance, it has $24$ elements in degree $3$ and $240$ elements in degree $7$.\nThe rest of the stable groups is much harder to understand.\n",
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