{
  "id": 242,
  "curve_key": "14857260430275850258959924889:-1867630771212539291861082918331060446874813",
  "ainvs": [
    "1",
    "0",
    "1",
    "-309526258964080213728331769",
    "2161609688903376164317636000643138896976"
  ],
  "rank_lower_bound": 18,
  "naive_height": 194.6664891321376,
  "faltings_height": 14.137281725412091,
  "conductor": "4599105032114305107130646860970904298444214155782477625288488806310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "127",
    "2804141",
    "94314161",
    "935018818255279",
    "15112931893627108554703387672603"
  ],
  "discriminant": "-120648124472674441798657772129443506216935731373216705396040170880065931985481700",
  "regulator": "663930766627720694.99921613424554549280042784189520445712829297273121330175",
  "points": [
    [
      "-34259847583749353581038809947044/1740884375734350625",
      "57715002807876692686002268734914592907285522529/2296967716638686767512359375"
    ],
    [
      "7525863514713",
      "16075189730766472378"
    ],
    [
      "-660198343256415048/37249",
      "-327862116505167218638695464/7189057"
    ],
    [
      "441204609390461774130/27804529",
      "5174310853255902398806508350454/146613281417"
    ],
    [
      "-29703234518830387/1681",
      "3168768482019896541111408/68921"
    ],
    [
      "67901882238708163545/4946176",
      "245881666667029467951608428843/11000295424"
    ],
    [
      "92226852264191646/1225",
      "27305643776116186645122701/42875"
    ],
    [
      "10689578885677356867/1682209",
      "-46351324941411708197844205556/2181825073"
    ],
    [
      "-27023096575177356/3721",
      "14402950374183416641536268/226981"
    ],
    [
      "91792253098923102966/7187761",
      "-329018460633611310010897992958/19270387241"
    ],
    [
      "437563141366809",
      "-9145667001043674681158"
    ],
    [
      "96577445967179930765719144/4431913354521",
      "-708384688894540163927332586316702566707/9330112744984508931"
    ],
    [
      "171621665403003489/12769",
      "-29899924168825630281171868/1442897"
    ],
    [
      "10464469825449",
      "-8276152107015445988"
    ],
    [
      "396411283986407896122/25270729",
      "-4338197160188729826225491076166/127035954683"
    ],
    [
      "60092165892459/4",
      "-240287988841674654337/8"
    ],
    [
      "11265307198908801/841",
      "499198982427503899130108/24389"
    ],
    [
      "17714909651077851/841",
      "-1722454784822183933725492/24389"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Rank >= 18 via 18 independent rational points with a positive-definite Neron-Tate height-pairing matrix. Mestre/Fermigier u4_v6 family, T=4694. Independently cross-verified in Sage and Magma; finite-field product independence backstop. Lower bound only; no exact-rank or upper-bound claim.",
  "created_at": "2026-06-29 18:45:02",
  "updated_at": "2026-07-01 22:32:42"
}