{
  "id": 3662,
  "curve_key": "272631968462528064:-142112722821259478531046912",
  "ainvs": [
    "0",
    "0",
    "0",
    "-5679832676302668",
    "164482318080161433485008"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 120.44069753916094,
  "faltings_height": 7.8295640713134524,
  "conductor": "1012399021707226560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "61",
    "101",
    "163",
    "443",
    "2477"
  ],
  "discriminant": "39476172672100594521611988742142189285113036800",
  "regulator": "814802.6112118405520630896109011864729018325394862835",
  "points": [
    [
      "-7354596",
      "453715089080"
    ],
    [
      "40983573",
      "23252371681"
    ],
    [
      "45200709",
      "9980366935"
    ],
    [
      "45272429",
      "11512700595"
    ],
    [
      "-3691258616718/51529",
      "5280049522681380392/11697083"
    ],
    [
      "1988518002/49",
      "9808794920408/343"
    ],
    [
      "82620195244/2025",
      "2345279850848528/91125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 107/256 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 19:28:58",
  "updated_at": "2026-09-29 19:28:58"
}