{
  "id": 3671,
  "curve_key": "190139921902114499889:-2632087963708013261878200506313",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3961248372960718748",
    "3046398107133845961154763606"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 140.09066044717537,
  "faltings_height": 9.49970833689783,
  "conductor": "18082853740749081030705",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "43",
    "89",
    "167",
    "227",
    "257",
    "1429",
    "8101"
  ],
  "discriminant": "-31089319686997066443492339123726659544632050995255376575",
  "regulator": "13177245.0808072624433585074477024246288888506432028890",
  "points": [
    [
      "-165337470",
      "60801572345107"
    ],
    [
      "-85442970840/121",
      "98633672055337862/1331"
    ],
    [
      "29706619261/16",
      "2927185674805233/64"
    ],
    [
      "101711508996/121",
      "23455434039076451/1331"
    ],
    [
      "314172219664/225",
      "52026095606770483/3375"
    ],
    [
      "434700373815/361",
      "32497214672774668/6859"
    ],
    [
      "2244894247440/2209",
      "870617521666124051/103823"
    ],
    [
      "5558658434715/2209",
      "9856146926316056546/103823"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -77/334 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 19:30:29",
  "updated_at": "2026-09-29 19:30:29"
}