{
  "id": 3666,
  "curve_key": "1398562439866216362513:-52300605541594680016528579672185",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-29136717497212840886",
    "60533108273018762726766844101"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 146.06919549983837,
  "faltings_height": 9.837889807319621,
  "conductor": "830429816548607909946",
  "bad_primes": [
    "2",
    "3",
    "13",
    "23",
    "29",
    "41",
    "53",
    "101",
    "883",
    "1613",
    "17021"
  ],
  "discriminant": "117177695264410553328821428175374613454602585923761633024",
  "regulator": "5410905.03338690483818208221308880725718759125399310593",
  "points": [
    [
      "-638467179",
      "280848465250983"
    ],
    [
      "3140672159",
      "1804178911125"
    ],
    [
      "3166266237",
      "4590615769523"
    ],
    [
      "14248118079/4",
      "352574749380135/8"
    ],
    [
      "-179184831007/121",
      "421810834882290273/1331"
    ],
    [
      "30415594609/9",
      "695152370727065/27"
    ],
    [
      "109998783148293/37249",
      "112046486866613106851/7189057"
    ],
    [
      "183331065552791/58081",
      "50060627137782104445/13997521"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -859/928 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 19:29:38",
  "updated_at": "2026-09-29 19:29:38"
}