{
  "id": 6399,
  "curve_key": "76656660332339012472274081:-659395193074459649227288250820776081521",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1597013756923729426505710",
    "763188880873084102125914053590356100"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 178.8041361785693,
  "faltings_height": 12.790444677767072,
  "conductor": "2446902750293324912726293074310",
  "bad_primes": [
    "2",
    "5",
    "7",
    "31",
    "37",
    "59",
    "67",
    "103",
    "109",
    "131",
    "12703",
    "144031",
    "2865043"
  ],
  "discriminant": "9057399872353381332958931741877083790158814474157544343339008000000000000",
  "regulator": "27190845073.94159123776589810055680012481921943198967970367",
  "points": [
    [
      "109433758350005503420/126315121",
      "245353778345585029038016315310/1419655644919"
    ],
    [
      "152541298072017486002186498780/132333499831298089",
      "32433944112183109162907392631621390347163370/48139846117749672664793813"
    ],
    [
      "1307367932062814708505129327933633479420/1538171401640850411644160961",
      "-8493701214408342333295361547514670877264629149288098574590/60326356847619743874910962209816946530209"
    ],
    [
      "183422831498923064/223729",
      "-7437902041942197227707786/105823817"
    ],
    [
      "2908852342320847580783740/3444858497089",
      "-827234930274933640283269315412983550/6393771050927587937"
    ],
    [
      "555396443081660/529",
      "-6007305334647098481970/12167"
    ],
    [
      "2300066159233373180/1216609",
      "2847008589304062024117091230/1341919727"
    ],
    [
      "177582718702416380/214369",
      "-9262053261541434999343970/99252847"
    ],
    [
      "745311037753469883307580/417480100129",
      "511948165139342187883393361664664670/269745164656050383"
    ],
    [
      "24450575358956814220/5612161",
      "-116285624441734153180584334590/13295209409"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = -431/80 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645",
  "created_at": "2026-11-02 01:20:13",
  "updated_at": "2026-11-02 01:20:13"
}