{
  "id": 3724,
  "curve_key": "678822025:7922127734875",
  "ainvs": [
    "1",
    "1",
    "0",
    "-14142125",
    "-9175021875"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 61.00760861328956,
  "faltings_height": 3.1387215651538596,
  "conductor": "2535958650",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29",
    "41",
    "59",
    "241"
  ],
  "discriminant": "144699441176471006250000",
  "regulator": "183.276346524853553709925926261228759381787485493",
  "points": [
    [
      "-3325",
      "34850"
    ],
    [
      "-2794",
      "93791"
    ],
    [
      "-1895",
      "104985"
    ],
    [
      "12605",
      "1341110"
    ],
    [
      "-152305/49",
      "24209030/343"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found 2026-09-30 in a direct search of the full rational 2-torsion family y^2 = x(x+da)(x+db), using the primitive smooth additive relation 2169 + 3776 = 5945 and twist d = -5. Candidates were screened by a deep Mestre–Nagao sieve and then checked with PARI/GP 2.17.4. The submitted five points are independent; PARI/GP ellrank with these points returned matching lower and upper bounds [5,5]. Conductor 2535958650.",
  "created_at": "2026-09-30 20:05:10",
  "updated_at": "2026-09-30 20:05:10"
}