{
  "id": 5578,
  "curve_key": "366247921:-6949505346281",
  "ainvs": [
    "1",
    "1",
    "1",
    "-7630165",
    "8040229730"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 59.15646312548679,
  "faltings_height": 2.7878826825623957,
  "conductor": "6741105",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "31",
    "109"
  ],
  "discriminant": "481464387762175400625",
  "regulator": "20.132560220694083386801614671858247889830046",
  "points": [
    [
      "-3092",
      "47193"
    ],
    [
      "-2627",
      "101133"
    ],
    [
      "8688",
      "768718"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Specialization at (u,v) = (31,140) of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), giving y^2 = x(x+961)(x+19600). Found in my own run scanning coprime positive integer pairs u < v, with v <= 250. The displayed global minimal model [1,1,1,-7630165,8040229730] is obtained by x = 4X - 6852, y = 8Y + 4X + 4. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.",
  "created_at": "2026-10-23 19:01:46",
  "updated_at": "2026-10-23 19:01:46"
}