{
  "id": 4588,
  "curve_key": "4031445326864915330669189329:-256101452121119862922430261839975461479833",
  "ainvs": [
    "1",
    "0",
    "0",
    "-83988444309685736055608111",
    "296413717732770620086157366281226224185"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 190.69278458018084,
  "faltings_height": 13.640364006648074,
  "conductor": "433617240451046823424614270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "31",
    "83",
    "193",
    "46411",
    "96469",
    "163477"
  ],
  "discriminant": "-38588711019421717367543442093484784060359339961983062702483516103574094643200",
  "regulator": "384430887.04259212732936148074068940777326907783434717002",
  "points": [
    [
      "5789185340326",
      "-2052237166951010051"
    ],
    [
      "2429212205321968918/292681",
      "-2071053561328653175732134479/158340421"
    ],
    [
      "5266648644736",
      "-400279169638395605"
    ],
    [
      "503344411278629758/109561",
      "99463231957754851042390711/36264691"
    ],
    [
      "429686976323571364/80089",
      "11057117426464697221867063/22665187"
    ],
    [
      "-4967498950345562129354/188692065769",
      "1416424326991173824201288893791951455/81965380373198603"
    ],
    [
      "-53126361192704522277410/14880828169",
      "42601155267291267706269882234128935/1815267585851803"
    ],
    [
      "677114861832118/841",
      "-369325466255380897772431/24389"
    ],
    [
      "20974200288871408/3721",
      "-327953814287400090609689/226981"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 467/305 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-18 14:10:25",
  "updated_at": "2026-10-18 14:10:25"
}