{
  "id": 4558,
  "curve_key": "7332976:-43665742360",
  "ainvs": [
    "0",
    "1",
    "1",
    "-152770",
    "50488130"
  ],
  "rank_lower_bound": 9,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 48.99965940785435,
  "faltings_height": 2.1314382877021045,
  "conductor": "875222414611247083",
  "bad_primes": [
    "875222414611247083"
  ],
  "discriminant": "-875222414611247083",
  "regulator": "1507325.4236644039146008723898494450525153887349470079156",
  "points": [
    [
      "-503",
      "566"
    ],
    [
      "-491",
      "2714"
    ],
    [
      "-486",
      "3190"
    ],
    [
      "-436",
      "5865"
    ],
    [
      "-414",
      "6553"
    ],
    [
      "-269",
      "8496"
    ],
    [
      "-65",
      "7755"
    ],
    [
      "2344",
      "112145"
    ],
    [
      "2759",
      "143660"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, records/rank_9.md: https://github.com/mrubinst/elliptic-curves-by-rank. Nine rational points checked exactly and certified independent modulo torsion. Fresh PARI rank bounds [9,9]. Trivial rational torsion. Conductor and absolute minimal discriminant both 875222414611247083. Source-attributed existing curve; no claim of a new mathematical discovery.",
  "created_at": "2026-10-18 01:52:56",
  "updated_at": "2026-10-18 01:52:56"
}