{
  "id": 3643,
  "curve_key": "4145971196617645214655574219825:-8515125893655048728545899512525892007430035625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-86374399929534275305324462913",
    "9855469784322937076113338981697664456740031"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 211.5163465673292,
  "faltings_height": 15.484894401303643,
  "conductor": "84518160226589403767572961475020918466832050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "47",
    "67",
    "71",
    "79",
    "97",
    "167",
    "173",
    "211",
    "313",
    "367",
    "431",
    "743",
    "1621",
    "4643",
    "5791"
  ],
  "discriminant": "-718721163078248688930564988199526733848361630919573154120071187972966941730914304000000",
  "regulator": "7126689268899172.85099538632183730278605038052372059139001175436114",
  "points": [
    [
      "-238644710244435",
      "4108179458614153564042"
    ],
    [
      "-188579236247435",
      "4408810495291602930392"
    ],
    [
      "173687088201055",
      "304968260589798877472"
    ],
    [
      "383895309535815",
      "5768322588638028403792"
    ],
    [
      "2930434854135415/9",
      "108845376563237961664064/27"
    ],
    [
      "8307885531825231/49",
      "99870495682830193816384/343"
    ],
    [
      "13216661435690378215/729",
      "48042537208162462928295096256/19683"
    ],
    [
      "49779750086093919551/297025",
      "47740671665086070458331478464/161878625"
    ],
    [
      "116441217397012396295/273529",
      "1013893524637339840183922511424/143055667"
    ],
    [
      "575473705287041346335/3996001",
      "5072480924666665759194444175168/7988005999"
    ],
    [
      "590497480367429852135/2968729",
      "3774508988974582188978953920064/5115120067"
    ],
    [
      "174805508556681069035595/1068439969",
      "11225569723415773685968794742963316/34924097266703"
    ],
    [
      "258876945727843615189215/2778238681",
      "236855560385929576557970115798304368/146438182636829"
    ],
    [
      "82798079153146389433990215/62374563001",
      "736336637403837876527580108926383702208/15577984734936749"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = 595/198 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 19:25:36",
  "updated_at": "2026-09-29 19:25:36"
}