{
  "id": 4297,
  "curve_key": "137892433:-1552925555065",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2872759",
    "1797128144"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 56.2259534044845,
  "faltings_height": 2.615302813565338,
  "conductor": "31433727",
  "bad_primes": [
    "3",
    "13",
    "61",
    "73",
    "181"
  ],
  "discriminant": "121732344670410283329",
  "regulator": "1315.432302400853825474662425493726926924390026",
  "points": [
    [
      "4061",
      "-241003"
    ],
    [
      "1712",
      "42704"
    ],
    [
      "11797/9",
      "437402/27"
    ],
    [
      "127024/9",
      "-45149776/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve#4065, submitted by NDElkies. This isogenous curve has the same rank and conductor, with torsion subgroup Z/2 x Z/2. The four supplied points were transported from the source curve.",
  "created_at": "2026-10-16 19:03:11",
  "updated_at": "2026-10-16 19:03:11"
}