{
  "id": 681,
  "curve_key": "10888324747456:-39082240567027776896",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-226840098905",
    "45234150343722525"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "naive_height": 90.22439966450949,
  "faltings_height": 5.480717761413487,
  "conductor": "190048676194583852124740520",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "1257331",
    "5891203",
    "30544424821"
  ],
  "discriminant": "-136892061462958748685450596556000000",
  "regulator": "22908317.713693262913394908649707061460954505897941124148453559",
  "points": [
    [
      "156635",
      "116387250"
    ],
    [
      "-394615",
      "270737250"
    ],
    [
      "214385",
      "80351250"
    ],
    [
      "182885",
      "99324750"
    ],
    [
      "330585",
      "79828350"
    ],
    [
      "604985",
      "359760450"
    ],
    [
      "264435",
      "61159350"
    ],
    [
      "239585",
      "68110350"
    ],
    [
      "345635",
      "90116250"
    ],
    [
      "233285",
      "70792050"
    ],
    [
      "278645",
      "60506670"
    ],
    [
      "302165",
      "65419410"
    ]
  ],
  "submitter": "NDElkies",
  "history": [],
  "commentary": "Found in the output of the searches from earlier this year that found Curves 157, 158, 244  of ranks 12, 13, 14.  This one is of interest for having many integral points (at least 650 pairs), thanks in part to large Tamagawa number 240 (with |Δ|/N = 7203000 = 2^5 3 5^5 7^4).",
  "created_at": "2026-09-08 19:53:10",
  "updated_at": "2026-09-08 19:53:10"
}