{
  "id": 3051,
  "curve_key": "88316473465865116039887837224229601:-25810359269655313250048045511606037348009231279376849",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1839926530538856584164329942171450",
    "29873101006545500680178813099094522047280615853767"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4,
    2
  ],
  "naive_height": 241.3987041644404,
  "faltings_height": 18.004192435216133,
  "conductor": "65784691229449019755350055710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "31",
    "37",
    "53",
    "61",
    "83",
    "89",
    "127",
    "433",
    "953",
    "61417"
  ],
  "discriminant": "13122765432207051703735070901124124545461382246320371005216153266367862989972859970779715993600000000",
  "regulator": "9112957.89489753138398156108279028056564737610971624288",
  "points": [
    [
      "26323375698764171202167333953/25155812020249",
      "-667021836484603198293626629988119570752973537/126170409068844013693"
    ],
    [
      "19030865410291017",
      "1322946856454299639383371"
    ],
    [
      "30274902252940537",
      "1385122149841520915844731"
    ],
    [
      "21934709591986537",
      "261392959659972909942731"
    ],
    [
      "27970127422757481",
      "540311127564830747685579"
    ],
    [
      "-11536576828500983",
      "-7040179091594253740552629"
    ],
    [
      "-7032549128278607/9",
      "-151080217417016534407570583/27"
    ],
    [
      "27003268326679874557/961",
      "17843511340482205241180959721/29791"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Voznyy (2021). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 30). Published independent points; exact point coordinates checked. One witness is a half of a published relation, giving a 2-saturated independent set.",
  "created_at": "2026-09-26 20:34:59",
  "updated_at": "2026-09-26 20:34:59"
}