{
  "id": 3645,
  "curve_key": "22121062415984398224790895911281:-98795125702913254222755922998894896097060669321",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-460855466999674963016476998152",
    "114346210304297863156871290426720957935291979"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 216.5222489849335,
  "faltings_height": 15.98341554656594,
  "conductor": "12334433622321215895724716304610404854359954238330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "37",
    "43",
    "59",
    "67",
    "97",
    "137",
    "151",
    "157",
    "449",
    "631",
    "11551",
    "172351",
    "356533",
    "66670921"
  ],
  "discriminant": "615899793300954530501810881212149850519364092250613667385586567435386111486671360000000000",
  "regulator": "1474443188037194718.4180034984213254134674559227298627471641692317271",
  "points": [
    [
      "500377196720737",
      "3004621962976095962381"
    ],
    [
      "510232259383039",
      "3469178130626886039287"
    ],
    [
      "771611998707149",
      "14769930934745969270873"
    ],
    [
      "972614224161487",
      "24211230454173535299881"
    ],
    [
      "-16997923422676499677715147/23001665569",
      "24998400109735179669722872576776781607/3488501605191247"
    ],
    [
      "-1965470045313711707/11449",
      "16814923987923146188227278683/1225043"
    ],
    [
      "-82575272110633243/121",
      "14024423438722708344713531/1331"
    ],
    [
      "118962591094178053/169",
      "25877659521017541478914557/2197"
    ],
    [
      "415992646427510557/361",
      "228872960220413725272363779/6859"
    ],
    [
      "505804140331391767/841",
      "180417793995221963535548659/24389"
    ],
    [
      "167051245226477568613/66049",
      "2087785399375569396967997508433/16974593"
    ],
    [
      "362706393811116758893/1520289",
      "7947634909249770703200697117897/1874516337"
    ],
    [
      "865769947136977192201/5329",
      "25474165930487603658452034170969/389017"
    ],
    [
      "2259143602660144643509/7209225",
      "16210790235559601053595801092253/19356769125"
    ],
    [
      "3066581192810895907237/6446521",
      "27205264631705234617670722523099/16367716819"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -419/177 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 19:26:06",
  "updated_at": "2026-09-29 19:26:06"
}