{
  "id": 4174,
  "curve_key": "1655295969464621257761:-193883658967671651769114417592241",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-34485332697179609537",
    "224402383073056115314473626449"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 148.68962214590434,
  "faltings_height": 10.443969975696204,
  "conductor": "760652629382499837073532406180848996486496990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "41",
    "8753",
    "305852722779866160643512871771605391"
  ],
  "discriminant": "-19129256019360117175069691888990082620036082051120489676800000",
  "regulator": "2511252938081386296.583470426742340388215830671178595415306361282686808",
  "points": [
    [
      "-7632680393",
      "207258880854596"
    ],
    [
      "-2019046403",
      "534602851710746"
    ],
    [
      "57904976857",
      "13870159463206046"
    ],
    [
      "420383656957",
      "272537758012325096"
    ],
    [
      "-30229700730897833/4363921",
      "3298056579321221900147444/9116230969"
    ],
    [
      "-29519496827733473/9803161",
      "16838029039901403613868236/30693697091"
    ],
    [
      "-2973375710795897/579121",
      "227347981775228586602788/440711081"
    ],
    [
      "-1393874944987793/1692601",
      "1105965951807859412769796/2202073901"
    ],
    [
      "-280054675219937/38809",
      "2387033464165085984308/7645373"
    ],
    [
      "-10070052520957/2209",
      "55608516350617458748/103823"
    ],
    [
      "-926622619073/121",
      "264142463131725196/1331"
    ],
    [
      "-713555528641/121",
      "628097488062045068/1331"
    ],
    [
      "244555844443/9",
      "118771503453203692/27"
    ],
    [
      "4667795361119/25",
      "10079982803555842868/125"
    ],
    [
      "24789889062433/169",
      "123332763971948831912/2197"
    ],
    [
      "609677274950076157/104060401",
      "501806972816879294498397146/1061520150601"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 1/9 of the K3 elliptic fibration y^2 + (Lx+B)y = x(x+D)(x+E) given in the commentary of database curve #3593; points from PARI ellrank.",
  "created_at": "2026-10-11 22:58:17",
  "updated_at": "2026-10-11 22:58:17"
}