{
  "id": 3655,
  "curve_key": "129906331381384159489891202355010561:-46249289222724407973602011138476509497223252283517441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2706381903778836656039400049062720",
    "53529269933708805299470502391666979470354686054400"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 242.55636519515593,
  "faltings_height": 18.08699621318136,
  "conductor": "4657372890037610572108520563138067741151339367609178987970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "31",
    "37",
    "43",
    "59",
    "79",
    "103",
    "113",
    "257",
    "271",
    "601",
    "1051",
    "2797",
    "4919",
    "81013",
    "270071",
    "599413",
    "1520587"
  ],
  "discriminant": "30820409949698128285263975281254460997877068798364715878074874853402716869542741888187690553344000000",
  "regulator": "1102572221540489776321.799250889128892802909038557606138733181273381146",
  "points": [
    [
      "-2444046140789992946886720/143017681",
      "16651828122563729682860030248908178560/1710348447079"
    ],
    [
      "-2076774779730084522360/657721",
      "4201553727509615618081412340404480/533411731"
    ],
    [
      "-25977384715861011210/3721",
      "1927108165601262954032226304230/226981"
    ],
    [
      "2135076990478270689/64",
      "311745418559039860277318979/512"
    ],
    [
      "271925412154445852301/10000",
      "207282615316348628231529371499/1000000"
    ],
    [
      "108225208733951064524520/2301289",
      "19204781562837876115380502355953920/3491055413"
    ],
    [
      "176834239890189215404800/5340721",
      "5774056458550050561959509574393280/12342406231"
    ],
    [
      "1775644256142638001637955/1811716",
      "2362836415839724165861226030852895415/2438569736"
    ],
    [
      "1575854446583075401302528/45738169",
      "336445051947159598333610044353507264/309327236947"
    ],
    [
      "1691720375353861939340160/35129329",
      "1229655154972523797314657691180319040/208211532983"
    ],
    [
      "18096175034864370351464880/133148521",
      "72000571228563946467976336663992531120/1536400783819"
    ],
    [
      "1731776776819240223845947648/29387216329",
      "50046035415357575609060600250020858121408/5037762333631483"
    ],
    [
      "1928799843893888043256928220/142815212281",
      "237972255189638450521361226188291950906320/53971154057900429"
    ],
    [
      "1976208709812282482164086240/47777653561",
      "36703551513464631230946551312248850297280/10443287293016941"
    ],
    [
      "3272723992107066014754499200/86789749201",
      "57711903370207855967938473354638658889920/25568346904363801"
    ],
    [
      "12840002751040210974917164800/392450878681",
      "17659385451964071789582345819721118819520/245854385007620579"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 477/1130 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 19:27:47",
  "updated_at": "2026-09-29 19:27:47"
}