{
  "id": 3685,
  "curve_key": "59700666401004628400084237210913:-460242580674801209321489924141393368303982817585",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1243763883354263091668421608561",
    "532688172077316525433436028544237463753530401"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 219.50068791796056,
  "faltings_height": 16.095808704089137,
  "conductor": "95872894991771433812104612981479282",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "29",
    "37",
    "41",
    "71",
    "101",
    "113",
    "251",
    "467",
    "2423",
    "7457",
    "218191"
  ],
  "discriminant": "555593375466277202100027124421552931318124517202290536775490822304701580710760091733786624",
  "regulator": "44363486949.69312922174808244502999394905507314224938794518",
  "points": [
    [
      "-721122679420513",
      "32474571970896280104564"
    ],
    [
      "676534503526967",
      "942396679375966862004"
    ],
    [
      "689781376045847",
      "1720420381425131473044"
    ],
    [
      "-1116499359109385389561/1203409",
      "39339637971987601568404710127860/1320139673"
    ],
    [
      "-3954145313922681/25",
      "3366777851546307588571812/125"
    ],
    [
      "730610578829108231/625",
      "406301702175705239745659796/15625"
    ],
    [
      "886791538033151759/1849",
      "542115465313604186193114540/79507"
    ],
    [
      "145238038976986662779/237169",
      "95243017038484714043532135660/115501303"
    ],
    [
      "1173820448894283788903/1745041",
      "1489481265745030271069768783988/2305199161"
    ],
    [
      "2149845742600104296091/3214849",
      "205070003524033720930962100660/5764224257"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 610/833 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:32:50",
  "updated_at": "2026-09-29 19:32:50"
}