{
  "id": 46,
  "curve_key": "0:422900683701240536042074298275176",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-489468383913472842641289697078"
  ],
  "rank_lower_bound": 16,
  "naive_height": 150.24938030199138,
  "faltings_height": 10.578437600957578,
  "conductor": "141972917837550720141347359033819641029697926227598433712323",
  "bad_primes": [
    "3",
    "41",
    "1768630113508483622913422573"
  ],
  "discriminant": "-103498257103574474983042224735654518310649788219919258176283467",
  "regulator": "359787206510825092.8999100746454939974782593912647860402619044739747445",
  "points": [
    [
      "7902580710",
      "63670717606558"
    ],
    [
      "9243066342",
      "547910842668385"
    ],
    [
      "9384872862",
      "580613609811649"
    ],
    [
      "10588813590",
      "835332795310558"
    ],
    [
      "11276039694",
      "971735349657982"
    ],
    [
      "14415958344",
      "1583178444925222"
    ],
    [
      "14600918460",
      "1619646563246566"
    ],
    [
      "38242987644",
      "7445931730687462"
    ],
    [
      "31840756833/4",
      "977373412490165/8"
    ],
    [
      "32498192145/4",
      "1731017073186653/8"
    ],
    [
      "7916896660",
      "82103281566566"
    ],
    [
      "8045520694",
      "176978571769182"
    ],
    [
      "8702884360",
      "411934199691558"
    ],
    [
      "12861701800",
      "1279905353076441"
    ],
    [
      "22606480144",
      "3326205023518937"
    ],
    [
      "202406423745/4",
      "90889676714539589/8"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Rank 16 Mordell curve from Noam D. Elkies, \"Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds\", ANTS XVI. This is the minimal model (8) for E_{-432D}, with D = 72513834653847828539450325493 = 41 * 1768630113508483622913422573: y^2 + y = x^3 - 489468383913472842641289697078. The 16 submitted points are the independent points Q_j in table (9); the paper gives conductor 27D^2 and discriminant -3^9 D^2.",
  "created_at": "2026-05-28 05:22:23",
  "updated_at": "2026-07-01 22:37:39"
}