{
  "id": 6402,
  "curve_key": "506970014512300696161:-10569331433657396595979736144145",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-10561875302339597837",
    "12233022495299492663524408885"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 143.02495059828368,
  "faltings_height": 9.877579316828573,
  "conductor": "3840861332482897807031772359312847844502330538",
  "bad_primes": [
    "2",
    "3",
    "13",
    "73",
    "139",
    "18083623",
    "89089283",
    "139790951",
    "7182657247932809"
  ],
  "discriminant": "10758075343847102648809637286729399096654666350316108644352",
  "regulator": "349714321716417.769409700898702031133937063652232658783948281038957229480",
  "points": [
    [
      "3508501871",
      "135515279952632"
    ],
    [
      "69923449180831/3025",
      "-579188081444817944536/166375"
    ],
    [
      "-64644454729/25",
      "18647603148446104/125"
    ],
    [
      "86598886559/25",
      "16398675873741488/125"
    ],
    [
      "1651883153119/625",
      "823916784214524728/15625"
    ],
    [
      "5902869167",
      "394416149577560"
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    [
      "7572657263",
      "605394129656984"
    ],
    [
      "-118463852513/49",
      "52734187497621512/343"
    ],
    [
      "226967225911/25",
      "-101906938895823656/125"
    ],
    [
      "18023639143",
      "-2382628794543016"
    ],
    [
      "-4963905393217/1681",
      "-9162057001201649288/68921"
    ],
    [
      "20034373781/16",
      "1994461586427383/64"
    ],
    [
      "155361380359/25",
      "-53996277467266808/125"
    ],
    [
      "1207340747",
      "35229305373020"
    ],
    [
      "22728963727",
      "3393229984338680"
    ],
    [
      "-94783179809/49",
      "54693086949112520/343"
    ],
    [
      "1525691031775/289",
      "1581380831523109432/4913"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 139/35 of the elliptic fibration of X637 given by:\r\ny^2 + (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pE + qD + pq(L-p-q),\r\nL = 4200T^2 + 38T - 141,\r\np = -407T + 3117,\r\nq = -6825T^2 - 7432T,\r\nD = 1055775T^3 - 16146795T^2 - 4120746T + 2212056,\r\nE = -1475250T^3 - 30473776T^2 - 36505848T.",
  "created_at": "2026-11-02 01:47:28",
  "updated_at": "2026-11-02 01:47:28"
}