{
  "id": 3269,
  "curve_key": "3856528:6760543040",
  "ainvs": [
    "0",
    "1",
    "0",
    "-80344",
    "-7851484"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 45.495833564397515,
  "faltings_height": 1.7687040441170705,
  "conductor": "85008",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23"
  ],
  "discriminant": "6743321251881984",
  "regulator": "5.21580662531964353581616925654681600406768",
  "points": [
    [
      "344",
      "2310"
    ],
    [
      "470",
      "7644"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 85008t3 = LMFDB 85008.bt3: https://www.lmfdb.org/EllipticCurve/Q/85008/bt/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 85008, minimal discriminant 6743321251881984, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:49:00",
  "updated_at": "2026-09-26 20:49:00"
}