{
  "id": 1763,
  "curve_key": "494650413152272030256656:-344593425013850470525186955648117696",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-10305216940672333963680",
    "398834982658354598384375680358400"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4,
    2
  ],
  "naive_height": 163.6744146896564,
  "faltings_height": 11.502436886449056,
  "conductor": "140233810193909992560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "43",
    "53",
    "79",
    "101",
    "149"
  ],
  "discriminant": "1322890813477155550797401760434272274862687898175567556000000000000",
  "regulator": "2120.60868924969973469840340741125353597634593340",
  "points": [
    [
      "-29027554830",
      "25952102911412370"
    ],
    [
      "6769288560",
      "18148999598730000"
    ],
    [
      "64663845280",
      "1687087657295040"
    ],
    [
      "79081528560",
      "8857184085750000"
    ],
    [
      "137790343010",
      "39937296741635150"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Specialization t=-3/2 of the generic rank-4 family with torsion Z/2Z x Z/4Z constructed by Dujella and Peral (LMS J. Comput. Math. 17 (2014), 282-288). The listed global minimal model has PARI/GP 2.17.4 rank bounds [5,5], torsion Z/2Z x Z/4Z, conductor 140233810193909992560 and minimal discriminant 1322890813477155550797401760434272274862687898175567556000000000000. The five listed rational points are independent; their canonical-height pairing determinant is approximately 2120.6086892497. Against the database snapshot of 2026-09-25, this improves the absolute discriminant of the existing rank-5 Z/2Z x Z/4Z entry #1376 by a factor of approximately 4.153307779e8.",
  "created_at": "2026-09-25 13:41:24",
  "updated_at": "2026-09-25 13:41:24"
}