{
  "id": 3606,
  "curve_key": "547074790773473865032256:-400703768335390779811306121475972096",
  "ainvs": [
    "0",
    "0",
    "0",
    "-11397391474447372188172",
    "463777509647443032189011714671264"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 163.9766174249086,
  "faltings_height": 11.52871097733873,
  "conductor": "41722361591357616334861316339541426195047099689760",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "19",
    "29",
    "41",
    "53",
    "1523005730143047156865092716375187737249"
  ],
  "discriminant": "1835044235562837506855515930668865977031841012175476158638323200000",
  "regulator": "215341763646059855314.840139823971270961993136977035053121819702039267563",
  "points": [
    [
      "7319335368508028",
      "626191935404329734347380"
    ],
    [
      "-1949685829179332/17161",
      "38428899118225276276460/2248091"
    ],
    [
      "-58814855750039/1024",
      "998711111138359809355/32768"
    ],
    [
      "5987754476050/81",
      "3660129879609506732/729"
    ],
    [
      "36490159309906/729",
      "85101814847407760740/19683"
    ],
    [
      "48516824569372/729",
      "3376535551140904100/19683"
    ],
    [
      "60642418468493/361",
      "393393096627944593115/6859"
    ],
    [
      "139230143135794/2025",
      "207270378805158581572/91125"
    ],
    [
      "1885064929831738/35721",
      "20564877378990458619820/6751269"
    ],
    [
      "2418106676294202/6889",
      "113942621328583088830100/571787"
    ],
    [
      "3895162420762370/18769",
      "215698422319516182974356/2571353"
    ],
    [
      "8963362779086652/134689",
      "7315303691287088454100/49430863"
    ],
    [
      "28249780747726690/1734489",
      "38392081611318671195127844/2284322013"
    ],
    [
      "267031976777775452/1408969",
      "119567346715650282502006460/1672446203"
    ],
    [
      "11573261326783665337/92698384",
      "28037360604527667430943050925/892500041152"
    ],
    [
      "147165954573088383708/20632736881",
      "57989291065487440375834510435900/2963706958323721"
    ],
    [
      "4241581762787104209458/58293756481",
      "62478552503434249180377499277300/14074502858529121"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 4/5 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:18:04",
  "updated_at": "2026-09-29 19:18:04"
}