{
  "id": 3668,
  "curve_key": "1951347185855128910656:-86198873998914175028681941986304",
  "ainvs": [
    "0",
    "1",
    "0",
    "-40653066371981852305",
    "99767215262970013788832370975"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 147.06842085436398,
  "faltings_height": 9.809141731519663,
  "conductor": "6913619279132804573280",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "41",
    "59",
    "67",
    "97",
    "137",
    "419",
    "50033"
  ],
  "discriminant": "4492840643437444928902245022525569668498451000000000000",
  "regulator": "2377942.42639535674411903786424790127261954615225766259",
  "points": [
    [
      "3676736690",
      "406164886875"
    ],
    [
      "3678737315",
      "115276012500"
    ],
    [
      "3797207315",
      "12255776032500"
    ],
    [
      "40050327185/49",
      "88839868033702500/343"
    ],
    [
      "327994438315/121",
      "129640534871490300/1331"
    ],
    [
      "640171045115/169",
      "24777076709704740/2197"
    ],
    [
      "721083090365/196",
      "34242487459125/2744"
    ],
    [
      "106550621894915/32041",
      "210915819716901997500/5735339"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 137/54 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:29:58",
  "updated_at": "2026-09-29 19:29:58"
}