{
  "id": 6214,
  "curve_key": "0:1610941758082603272",
  "ainvs": [
    "0",
    "0",
    "1",
    "0",
    "-1864515923706717"
  ],
  "rank_lower_bound": 11,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 83.84670124957044,
  "faltings_height": 5.044881013255833,
  "conductor": "1501813280054553636823661835963603",
  "bad_primes": [
    "3",
    "2027",
    "596069",
    "6172709"
  ],
  "discriminant": "-1501813280054553636823661835963603",
  "regulator": "256851610349.286783858920371669859901975962333545055064354205",
  "points": [
    [
      "138243",
      "27883034"
    ],
    [
      "154599",
      "42784713"
    ],
    [
      "189747",
      "70477802"
    ],
    [
      "303447",
      "161483462"
    ],
    [
      "7143657/4",
      "19090170207/8"
    ],
    [
      "1982577/16",
      "394566633/64"
    ],
    [
      "2724393/16",
      "3547428875/64"
    ],
    [
      "27756013/81",
      "142801429375/729"
    ],
    [
      "66277381/225",
      "519517147904/3375"
    ],
    [
      "673149799/1521",
      "17276112191242/59319"
    ],
    [
      "937917967/7569",
      "4071142690802/658503"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Generic-rank-4 Burkhardt fibration from quartic coordinates (-4, -5, 9, -12, -3), specialized at t=-844/331. PARI/GP 2.17.4 returned rank bounds [11,11].",
  "created_at": "2026-10-30 19:33:12",
  "updated_at": "2026-10-30 19:33:12"
}