{
  "id": 6372,
  "curve_key": "310744412728203810496:-3694425152763889320640431251840",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-6473841931837579385",
    "4275955040079115505798210781"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 141.55650727249346,
  "faltings_height": 9.828623065051397,
  "conductor": "98604798131699903972915030384706682823384424470877778872",
  "bad_primes": [
    "2",
    "3",
    "267671",
    "7942445005349047",
    "1932552357343601932676956591016269"
  ],
  "discriminant": "9466060620643190781399842916931841551044904749204266771712",
  "regulator": "166925853806722454.1623117397733732179880193041954963412736215730068319964076",
  "points": [
    [
      "674175653",
      "-14760416627862"
    ],
    [
      "338806073",
      "-46059412460442"
    ],
    [
      "2230990793",
      "-30614183015622"
    ],
    [
      "-1133012437",
      "-100779119511402"
    ],
    [
      "584347149",
      "26315700080358"
    ],
    [
      "443123865",
      "38655561491034"
    ],
    [
      "-2817016759",
      "-12577947419706"
    ],
    [
      "-1562478541",
      "-102842860892658"
    ],
    [
      "3713401745",
      "177317187009834"
    ],
    [
      "-2082708397",
      "-93407544496338"
    ],
    [
      "703954604",
      "8216469892767"
    ],
    [
      "2273281147",
      "-36152051684710"
    ],
    [
      "-1722289091",
      "-101572590705658"
    ],
    [
      "-2616313829",
      "-57485933170054"
    ],
    [
      "5002138197",
      "-311533844661450"
    ],
    [
      "10864440371",
      "-1102876724972046"
    ],
    [
      "3218329044",
      "-129519500696283"
    ],
    [
      "11500660861",
      "1204557888211066"
    ],
    [
      "18134438147",
      "2418786628151010"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Layr-Labs/elliptic-rank-challenge-public,\r\nsubmission/board/1-19-m10-a.ec, commit\r\ndebf8f35561f00231e8c084c95b7d4e68337de78.\r\n\r\nThe public file contains 19 rational points on the displayed minimal model.\r\nAll 19 points were checked exactly. The minimal discriminant is\r\n9466060620643190781399842916931841551044904749204266771712.\r\nThe conductor is 98604798131699903972915030384706682823384424470877778872.\r\nNaive height is 141.55650727249346. Source attribution remains with Layr-Labs.",
  "created_at": "2026-11-01 19:43:38",
  "updated_at": "2026-11-01 19:43:38"
}