{
  "id": 3687,
  "curve_key": "149929914520267991547007331073600:-1835673261899835119969107095607050232919615424000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-3123539885838916490562652730700",
    "2124621830902586944408688768063715547360666000"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 222.26316221459123,
  "faltings_height": 16.21262733013603,
  "conductor": "187455817312613230634302607218785600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "31",
    "43",
    "71",
    "89",
    "101",
    "137",
    "151",
    "317",
    "359",
    "557",
    "23773",
    "70121"
  ],
  "discriminant": "332821590487182885899159211171165207380796777356606522812117012946714310908854364160000000",
  "regulator": "42016251504.34224951999012235546193395594956534102073482765",
  "points": [
    [
      "-1950332338601230",
      "28247050862142209168400"
    ],
    [
      "-164349407766190",
      "51317975058955534465200"
    ],
    [
      "1007861884074245",
      "544612158496118690775"
    ],
    [
      "1033634668656845",
      "598870052946853870275"
    ],
    [
      "177987925635835520/361",
      "182046805675652994234687900/6859"
    ],
    [
      "2158271962342471810/2601",
      "1353414578148616055548193200/132651"
    ],
    [
      "37529110310662240370/36481",
      "1258326583654763301729296400/6967871"
    ],
    [
      "46068797956252024640/18769",
      "247243711779369533077512686100/2571353"
    ],
    [
      "62474820767094228770/121801",
      "1089932630686338004828193811600/42508549"
    ],
    [
      "2172885329090136251105/2184484",
      "4358478099884026353677087122575/3228667352"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -1877/1424 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 19:33:10",
  "updated_at": "2026-09-29 19:33:10"
}