{
  "id": 3651,
  "curve_key": "2145608408406940059033456738472161:-97292343315424252272313812525189510886658396801745",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-44700175175144584563197015384837",
    "112606878837296599453184780505115482103256620285"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 230.24619366374444,
  "faltings_height": 17.085688183723647,
  "conductor": "373194485014698697229027713931389442079902239969278",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "31",
    "37",
    "59",
    "109",
    "167",
    "181",
    "283",
    "983",
    "2221",
    "3163",
    "6563",
    "7867",
    "43117",
    "859378921"
  ],
  "discriminant": "238309517520333455096908703517660122164915444286578516241861572754946754199381531956425079652352",
  "regulator": "30866841244057419.312801466735732569602608922663008068324935307995775",
  "points": [
    [
      "-6674497450763009",
      "337070405992539082633472"
    ],
    [
      "3370317424408375",
      "15384030974988478275560"
    ],
    [
      "4712529176184991",
      "81311270159101668469472"
    ],
    [
      "5547697914584959",
      "188055955665835775594240"
    ],
    [
      "195317847999145459",
      "86270356969368338446219340"
    ],
    [
      "-509986188707079721/625",
      "6021971894336665627147381408/15625"
    ],
    [
      "-50640995165925689/25",
      "55176095225381211889288576/125"
    ],
    [
      "-15645192302294681/9",
      "11614976509186423313374144/27"
    ],
    [
      "517116188387614039/169",
      "147039860879691871186214144/2197"
    ],
    [
      "963524197526109079/289",
      "123884510840525079307022056/4913"
    ],
    [
      "21086036830735608823/3721",
      "46113459407310498803541749504/226981"
    ],
    [
      "34596284014333506535/10201",
      "4197544081312655329120248640/1030301"
    ],
    [
      "48266542259758564903/10201",
      "86408116035293547872379104512/1030301"
    ],
    [
      "54954793261166911517839/31798321",
      "36092964203786370015008508171573760/179310732119"
    ],
    [
      "2922556219235105732704285/44209201",
      "4971612774155090849503519241497919726/293946977449"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -1321/42 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 19:27:07",
  "updated_at": "2026-09-29 19:27:07"
}