{
  "id": 150,
  "curve_key": "83680761:-765901311885",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-1743349",
    "886895689"
  ],
  "rank_lower_bound": 9,
  "naive_height": 54.728638325455414,
  "faltings_height": 2.3120879913684127,
  "conductor": "183107934630169474",
  "bad_primes": [
    "2",
    "244254379",
    "374830403"
  ],
  "discriminant": "-366215869260338948",
  "regulator": "293591.30673220840727887138511462027952831615032133636905",
  "points": [
    [
      "-28",
      "-30575"
    ],
    [
      "56",
      "28069"
    ],
    [
      "-87",
      "-32173"
    ],
    [
      "130",
      "25673"
    ],
    [
      "-159",
      "-33980"
    ],
    [
      "176",
      "24109"
    ],
    [
      "264",
      "20963"
    ],
    [
      "-285",
      "-36743"
    ],
    [
      "-302",
      "-37075"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Found by the ec-smallcond GPU integral-point search (Elkies-Watkins style large-rank/small-conductor sweep); rank >= 9 certified from 9 independent points via PARI/GP ellrank (returned rank exactly 9).",
  "created_at": "2026-06-24 21:06:39",
  "updated_at": "2026-07-01 22:53:26"
}