{
  "id": 4294,
  "curve_key": "-81407:7690015",
  "ainvs": [
    "1",
    "1",
    "1",
    "1696",
    "-8194"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 33.921649630137786,
  "faltings_height": 0.9031837205102444,
  "conductor": "12190893",
  "bad_primes": [
    "3",
    "11",
    "13",
    "157",
    "181"
  ],
  "discriminant": "-346428606381",
  "regulator": "253.2841873318740887986455927155597930916538472",
  "points": [
    [
      "17",
      "152"
    ],
    [
      "25",
      "212"
    ],
    [
      "163/4",
      "2725/8"
    ],
    [
      "137",
      "1610"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve#4041, submitted by NDElkies. This isogenous curve has the same rank and conductor. The four supplied points were transported from the source curve.",
  "created_at": "2026-10-16 18:58:38",
  "updated_at": "2026-10-16 18:58:38"
}