{
  "id": 6191,
  "curve_key": "5750495582868349450755972610842049:-436236909414554243828850022599034390443236774277793",
  "ainvs": [
    "1",
    "0",
    "0",
    "-119801991309757280224082762725876",
    "504903830340919253707299361454294229524627150480"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 233.20453985941592,
  "faltings_height": 17.172853839770703,
  "conductor": "8286274652757291070116518242424271719730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "31",
    "73",
    "97",
    "211",
    "227",
    "271",
    "117721",
    "28016012371944271"
  ],
  "discriminant": "-83394833937982002001584379264645216187821964016393026831305398639950375461003274662279800422400",
  "regulator": "2499288656.92920652483135783332031743746919899566703495785646",
  "points": [
    [
      "-10818419459289496",
      "731302739156452064070860"
    ],
    [
      "-5617392527237272",
      "1000310587001780845141196"
    ],
    [
      "4107922084895848",
      "286509801625647625925836"
    ],
    [
      "4207309335114104",
      "274472724255912790908236"
    ],
    [
      "6305969564742248",
      "13949518252940993349836"
    ],
    [
      "6418472761602848",
      "19455161837760161685836"
    ],
    [
      "8192443057331024",
      "270698825446377471099620"
    ],
    [
      "8332723222370480",
      "291896555982341022396620"
    ],
    [
      "17186071910291048",
      "1876719134429111775429836"
    ],
    [
      "21943796647536164",
      "2905614266881716742401440"
    ],
    [
      "31451885859761768",
      "5277288602520047698291916"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = -961/194 of the elliptic fibration of X648 given by:\ny^2 + (Lx+B)y = x^3,\nwhere\nL = 3885067921T^2 - 14778309212T + 14171920816,\nB = 4936839685420991948803368000T^5 - 37762139727356747035718880000T^4 + 97681596151298882036363082000T^3 - 104946797327065126983361746000T^2 + 40090501217702000033914176000T.",
  "created_at": "2026-10-30 15:39:57",
  "updated_at": "2026-10-30 15:39:57"
}