{
  "id": 6435,
  "curve_key": "1670700127245411119451362543311849:-68288489889914129386993544141293217967111763259893",
  "ainvs": [
    "1",
    "0",
    "1",
    "-34806252650946064988570052985664",
    "79037604039252461667758510732843216192208273486"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 229.49565253574409,
  "faltings_height": 16.680325669257222,
  "conductor": "374179550932488127122381505424798097010",
  "bad_primes": [
    "2",
    "5",
    "7",
    "17",
    "29",
    "31",
    "41",
    "43",
    "61",
    "71",
    "109",
    "137",
    "173",
    "3234111343",
    "5482577311"
  ],
  "discriminant": "3101455465548163978207648307800022510843399534515837083730233446854219001824390381640667200",
  "regulator": "12669094259654.6488340157136681745291061008785762539265758425",
  "points": [
    [
      "5126596264299196703552882/1494054409",
      "146474391504822700575443101737305086/57749685071077"
    ],
    [
      "195415012818733495085906/36711481",
      "46968678690082005995386572812165074/222434863379"
    ],
    [
      "86911168562110130152640131650929/25451635426561969",
      "3412940514011260869370350799944699087665917733/4060444143050101772487703"
    ],
    [
      "304595507542415941804062915689/88506531499681",
      "-2972723305196454761285377131725207497122443/832650950483915414671"
    ],
    [
      "1635761923281474355778018/433514041",
      "340890604871717200630443794503064398/9026195847661"
    ],
    [
      "3179494544147180861876/790321",
      "45113989380790987607124142018513/702595369"
    ],
    [
      "191440768101641657812/56169",
      "249793309776168278458961674/13312053"
    ],
    [
      "18200773532215297391905/4626801",
      "544300151464806269217429067661917/9952248951"
    ],
    [
      "3227602887595252841/64",
      "5760544027255356564173990879/512"
    ],
    [
      "605401317837346639338532/175907169",
      "8351339201793767769279110483525591/2333056782447"
    ],
    [
      "382086369763131714523985729/13846934929",
      "-7310315508440288428810165482125651135573/1629410373900217"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "Voznyy (2026), T = 2186/195 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": "2026-11-03 04:27:19",
  "updated_at": "2026-11-03 04:27:19"
}