{
  "id": 3640,
  "curve_key": "1882151974876070806434917805121:-1152420994387820377126725721193416071782443105",
  "ainvs": [
    "1",
    "0",
    "0",
    "-39211499476584808467394120940",
    "1333820595356270317012457647091674096534416"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 209.12990573855456,
  "faltings_height": 15.482354785345334,
  "conductor": "304327139592757069203804262254572708025894",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "41",
    "53",
    "59",
    "97",
    "113",
    "157",
    "251",
    "271",
    "373",
    "431",
    "1471",
    "1523",
    "5569",
    "67751"
  ],
  "discriminant": "3089954745649663912334772067123912757220807681183573537767821297718018893444133356634112",
  "regulator": "146996379335206.703767163164132602416230222333620897378767678458845",
  "points": [
    [
      "-140148145316424",
      "2019039286251875890548"
    ],
    [
      "-88388380975496",
      "2027098167770009382580"
    ],
    [
      "-45657438921416",
      "1740384940487610288340"
    ],
    [
      "193670307863788",
      "1001967849743938185808"
    ],
    [
      "343197786067584",
      "5319772008421981751340"
    ],
    [
      "468438060110314",
      "9260507332124504125600"
    ],
    [
      "-59165253291925920440/310249",
      "236703185193410889964315457012/172808693"
    ],
    [
      "-3416617957242374696/16129",
      "751779883704445153311203884/2048383"
    ],
    [
      "-60909623840426774/2209",
      "160642428552230359217487200/103823"
    ],
    [
      "7323866022345208/9",
      "608732888150654179554908/27"
    ],
    [
      "49874703145357720/9",
      "11131270753803727089307612/27"
    ],
    [
      "627856720037590456/2209",
      "376493476293568849383245420/103823"
    ],
    [
      "2188654843421713240/97969",
      "20999435586510301866132657652/30664297"
    ],
    [
      "1434431601418880101912/48288601",
      "148269382800394110235857704372356/335557488349"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 853/2 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 19:25:01",
  "updated_at": "2026-09-29 19:25:01"
}