{
  "id": 3646,
  "curve_key": "1168378203404107553518800431680081:-39759309159548877195085630435746571986152868841945",
  "ainvs": [
    "1",
    "0",
    "0",
    "-24341212570918907364975008993335",
    "46017718934663050280692506168501437161981737641"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 228.42277411524177,
  "faltings_height": 16.8662862704206,
  "conductor": "44025871847742350339136611296547024333859559593162",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "53",
    "59",
    "137",
    "317",
    "379",
    "419",
    "647",
    "821",
    "1747",
    "2143",
    "2297",
    "4513",
    "5647",
    "10453",
    "191119"
  ],
  "discriminant": "8194057231660386994483052814756513318437208168868334196703642321903499457257297607798341763072",
  "regulator": "457530714498786658.75619102066173108788265258342396232814652616880289",
  "points": [
    [
      "2679684176319766",
      "5743208724939292751221"
    ],
    [
      "3830205657410930",
      "94746009226532528783681"
    ],
    [
      "248692530822412292",
      "123996459263874675185619989"
    ],
    [
      "-24357366219621893729194/12369289",
      "12780800324711069089205146322709305/43502789413"
    ],
    [
      "-5689713812753183550106/1026169",
      "106637181529781606685706325392561/1039509197"
    ],
    [
      "-3474886522146359304061/770884",
      "171425807990884197857194899480901/676836152"
    ],
    [
      "-10893684461757643546/4489",
      "90627209338751588956935955319/300763"
    ],
    [
      "1450448593689441038/961",
      "3359585621085550111111077683/29791"
    ],
    [
      "3617391324999309902/9409",
      "174881828890788008423472793997/912673"
    ],
    [
      "14661523308436763374/173889",
      "15204303785954660322126305820773/72511713"
    ],
    [
      "71365277967895836518/19321",
      "216566162988367157446427039951/2685619"
    ],
    [
      "1024993157877255420854/323761",
      "4829985843888039178710611304829/184220009"
    ],
    [
      "1524114951491195305814/289",
      "59501291886636930990369390776293/4913"
    ],
    [
      "261345408258091968329750/189310081",
      "319493036894756548050563346446048459/2604717404479"
    ],
    [
      "62290281358323173311179254/3667392481",
      "472830044484806929867950462519865063259/222093621256879"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -565/1078 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (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 19:26:16",
  "updated_at": "2026-09-29 19:26:16"
}