{
  "id": 1246,
  "curve_key": "11268143683216:32618088811470111040",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-234752993400",
    "-37752339354870384"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "naive_height": 90.15900215190149,
  "faltings_height": 5.50315611303578,
  "conductor": "72554931074823247344",
  "bad_primes": [
    "2",
    "3",
    "7",
    "47",
    "59",
    "71",
    "79",
    "139",
    "227",
    "239",
    "263"
  ],
  "discriminant": "212261836373132477107527360278341632",
  "regulator": "8017544.1097938529080858825522747036190702990147302935074",
  "points": [
    [
      "2112906",
      "2983124214"
    ],
    [
      "2144714",
      "3053525258"
    ],
    [
      "11704296",
      "40007404044"
    ],
    [
      "-106336014/529",
      "441022511286/12167"
    ],
    [
      "-8067984/25",
      "8288155764/125"
    ],
    [
      "5305072/9",
      "4572440684/27"
    ],
    [
      "6137890/9",
      "9327553858/27"
    ],
    [
      "10057729/9",
      "28260376228/27"
    ],
    [
      "365768616/625",
      "2485333294164/15625"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "The curve was found by adapting Dujella’s 2002 use of Fermigier’s rank-\\(\\ge 8\\) construction with rational 2-torsion. Dujella used products of three primes \\(p_i\\equiv1\\pmod4\\), giving four representations as sums of two squares. I instead used products of four such primes, giving eight representations and many possible Fermigier curves to test.\r\nhe best case came from \\(5\\cdot13\\cdot29\\cdot41\\), using \\((106,257)\\), \\((113,254)\\), \\((142,239)\\), and (166,223)",
  "created_at": "2026-09-24 14:56:47",
  "updated_at": "2026-09-24 14:56:47"
}