{
  "id": 3637,
  "curve_key": "3782367116212326064158481:-7351962176730168792891500309754473465",
  "ainvs": [
    "1",
    "1",
    "1",
    "-78799314921090126336635",
    "8509215482293751203148041509575561"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 169.77717680014229,
  "faltings_height": 11.900632218390228,
  "conductor": "455514655953569565656462935595492873046",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "37",
    "43",
    "71",
    "157",
    "631",
    "12721",
    "1299673",
    "11326561",
    "20456041"
  ],
  "discriminant": "34915865618761763073549337830972982408707179426408720321728921731072",
  "regulator": "520589953403783.4570444427791043737527034655893209553375956790392",
  "points": [
    [
      "136975485403",
      "16900049119712534"
    ],
    [
      "-21342102184229/121",
      "173135843458133284306/1331"
    ],
    [
      "-15783081350461/49",
      "7453908939379158698/343"
    ],
    [
      "12809124036063/169",
      "119774482860609802438/2197"
    ],
    [
      "160221606163411/225",
      "1889657427228542709946/3375"
    ],
    [
      "5860864089980091/37249",
      "17620391238430943288302/7189057"
    ],
    [
      "5875730590422265/136161",
      "3619324592691474753612928/50243409"
    ],
    [
      "10835622926510413/69169",
      "55622798740791208173538/18191447"
    ],
    [
      "11776358776075347/52441",
      "555310088664689933554822/12008989"
    ],
    [
      "108022578708368691/410881",
      "20339919858737708931107942/263374721"
    ],
    [
      "304675932725825699/5329",
      "168171334476281740427089654/389017"
    ],
    [
      "2908388942949335179/19193161",
      "582928367452960545245988734/84085238341"
    ],
    [
      "4015906108044053039/23863225",
      "440791490872502887069780642/116571854125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -265/63 of the rank-9 fibration of X400, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #802 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:24:17",
  "updated_at": "2026-09-29 19:24:17"
}