{
  "id": 2051,
  "curve_key": "40193073:184385317815",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-837356",
    "-213199594"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 52.52761567592624,
  "faltings_height": 2.4017887465797045,
  "conductor": "67158441",
  "bad_primes": [
    "3",
    "7",
    "37",
    "47",
    "613"
  ],
  "discriminant": "17901206848077859089",
  "regulator": "858.4620238092345509335929407323901819300564607",
  "points": [
    [
      "-716",
      "4705"
    ],
    [
      "26844/25",
      "-1463707/125"
    ],
    [
      "5500",
      "399162"
    ],
    [
      "-178671/256",
      "24189535/4096"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "2-isogenous partner of curve#1699 (Michael Rubinstein).",
  "created_at": "2026-09-26 05:09:09",
  "updated_at": "2026-09-26 05:09:09"
}