{
  "id": 6380,
  "curve_key": "10833458680036453215899935368716539632553:-1127381731078781156525075895513208044921057377077493247142165",
  "ainvs": [
    "1",
    "0",
    "1",
    "-225697055834092775331248653514927909012",
    "1304839966526367079292622346635594172566212354194928747330"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 276.5503739935,
  "faltings_height": 20.760875009922344,
  "conductor": "17153194934093648937888015864579548144183014877220462",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "31",
    "37",
    "43",
    "59",
    "97",
    "101",
    "173",
    "223",
    "283",
    "313",
    "509",
    "643",
    "811",
    "1669",
    "2441",
    "18353",
    "76631",
    "103183"
  ],
  "discriminant": "270024573229128276090006689864315816778965099908303459634493821980848652435175762095432595425899176908551239485584",
  "regulator": "8142477645586.214870950454589389898295603200189571854792031695427",
  "points": [
    [
      "22912384715375325141",
      "90344151648096795702348376999"
    ],
    [
      "7775533252773607578",
      "4474966614248503735112065483"
    ],
    [
      "7411142680723522734",
      "-6262919485115065915004223281"
    ],
    [
      "8359419010476971562",
      "1516231003151279402714485531"
    ],
    [
      "11903495092422888453",
      "17461398170801337815808108883"
    ],
    [
      "12209723706930009429",
      "19218079096910244710341616899"
    ],
    [
      "8469075908437793252277/121",
      "762740250152744505182392582796501/1331"
    ],
    [
      "4258252986937509593745933/1570009",
      "52515809699313093467398268998801438187/1967221277"
    ],
    [
      "-394298875157636929116/25",
      "3834828007652428883777940430238/125"
    ],
    [
      "9085588543251232962",
      "2060536464613842372263909971"
    ],
    [
      "202089129516245306628067149/34562641",
      "-2764317999400973381272593688838223776179/203193766439"
    ],
    [
      "8793230338234696149",
      "366400939753017510036707971"
    ],
    [
      "789796717265386896140685242121/92084937025",
      "-1670329765572057568976981467209050917378459/27943634564921375"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "From a public submission branch of the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, branch submissions/1823cd1b-9025-4448-aa7c-3f8e2c989879, file submission/board/x312-p-16288-q41497.ec; pull request #63, closed without merging), where it is recorded as a challenge participant's own find: the fibre T = -16288/41497 of the Z/2xZ/2 K3 fibration x312. Not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.",
  "created_at": "2026-11-01 21:17:58",
  "updated_at": "2026-11-01 21:17:58"
}