{
  "id": 2787,
  "curve_key": "10633:1037915",
  "ainvs": [
    "1",
    "0",
    "1",
    "-222",
    "-1220"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 27.81515295495326,
  "faltings_height": 0.2605947577449509,
  "conductor": "8502",
  "bad_primes": [
    "2",
    "3",
    "13",
    "109"
  ],
  "discriminant": "72284004",
  "regulator": "3.41755890818183821563630896792156575209707",
  "points": [
    [
      "19",
      "29"
    ],
    [
      "-8",
      "11"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 8502b2 = LMFDB 8502.b2: https://www.lmfdb.org/EllipticCurve/Q/8502/b/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 8502, minimal discriminant 72284004, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:22:25",
  "updated_at": "2026-09-26 20:22:25"
}