{
  "id": 3632,
  "curve_key": "11214565616461745934081:-772548567476540150051120871937665",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-233636783676286373627",
    "894153434637738073293054084075"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "naive_height": 152.3145011631787,
  "faltings_height": 10.728403240710502,
  "conductor": "3744534523427843486091406117969518",
  "bad_primes": [
    "2",
    "3",
    "11",
    "29",
    "31",
    "37",
    "163",
    "167",
    "199",
    "491",
    "1237",
    "2063",
    "3137",
    "4933",
    "5413"
  ],
  "discriminant": "470824754194661964974014144484184477065358692591847532708380672",
  "regulator": "175859167782.97162829868207457612908104326399647874335249846373",
  "points": [
    [
      "-8894264653",
      "1506183000190362"
    ],
    [
      "-4166105965",
      "1339852921415634"
    ],
    [
      "37038417131",
      "6561350226610266"
    ],
    [
      "63889280027",
      "15708344574285450"
    ],
    [
      "503428604555",
      "357032521890142554"
    ],
    [
      "-107391107628757/9409",
      "1314358402215245342106/912673"
    ],
    [
      "-1483401773317/121",
      "1842313037670777942/1331"
    ],
    [
      "-1245788111905/169",
      "3270402467580976038/2197"
    ],
    [
      "-148758444221/9",
      "13234350457065854/27"
    ],
    [
      "-12921500693/9",
      "29903436912618814/27"
    ],
    [
      "14005285583675/529",
      "44314556597849383350/12167"
    ],
    [
      "25606842889349/1225",
      "97244474520121145412/42875"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -55/109, u = 11/5 of the Elkies-Klagsbrun family y^2 = x^3 + 2A(t,u)x^2 + B(t,u)x (arXiv:2003.00077, Sec. 9, eqs. (3)-(4)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:23:22",
  "updated_at": "2026-09-29 19:23:22"
}