{
  "id": 6250,
  "curve_key": "12688661770005481:-1252389114995958821581685",
  "ainvs": [
    "1",
    "1",
    "0",
    "-264347120208447",
    "1449524328508096697385"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 111.23845564679952,
  "faltings_height": 7.254424932145549,
  "conductor": "152021288284679676420402639931235696997162",
  "bad_primes": [
    "2",
    "3",
    "7",
    "43",
    "84175685650431714518495370947528071427"
  ],
  "discriminant": "274550446642131495615247167715811668776874572",
  "regulator": "35959548414759.81327587371165044439191555781361220700150670271185051917",
  "points": [
    [
      "-11498008",
      "-54481910019"
    ],
    [
      "12661087364",
      "-1424649664640961"
    ],
    [
      "-243804642/169",
      "-93928254126933/2197"
    ],
    [
      "94734103022/4489",
      "-21836162944709475/300763"
    ],
    [
      "152738137/9",
      "-1161898286495/27"
    ],
    [
      "5239863896/361",
      "-177666113943879/6859"
    ],
    [
      "10065510398/841",
      "8090975755115/24389"
    ],
    [
      "1450399355/121",
      "2353402773255/1331"
    ],
    [
      "14158752958/1089",
      "521042042548967/35937"
    ],
    [
      "-17280562",
      "29288457507"
    ],
    [
      "-53008437/4",
      "409959709821/8"
    ],
    [
      "316932",
      "36956249661"
    ],
    [
      "12909921",
      "13721974275"
    ],
    [
      "26427614",
      "113657378347"
    ],
    [
      "33561359",
      "174281845689"
    ],
    [
      "420860814/25",
      "5258221573227/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 16 proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file mestre/mestre_rank_16.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 22:51:22",
  "updated_at": "2026-10-31 22:51:22"
}