{
  "id": 3758,
  "curve_key": "297568:-162320896",
  "ainvs": [
    "0",
    "1",
    "0",
    "-6199",
    "185805"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "naive_height": 37.81019414783377,
  "faltings_height": 0.7825132419455049,
  "conductor": "10135808",
  "bad_primes": [
    "2",
    "17",
    "137"
  ],
  "discriminant": "344617472",
  "regulator": "26.92692963232290526205801708356527807852925257",
  "points": [
    [
      "-91",
      "68"
    ],
    [
      "28",
      "187"
    ],
    [
      "37",
      "92"
    ],
    [
      "79",
      "442"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found 2026-10-01 in a discriminant-first search for rank-4 elliptic curves over Q with rational 2-torsion. The source model is y^2 = x^3 + 136*x^2 - 34*x. Its global minimal model has a-invariants [0,1,0,-6199,185805]. PARI/GP 2.17.4 gives exact rank bounds [4,4] and torsion Z/2Z. The minimal discriminant is 344617472 and the conductor is 10135808. The four submitted rational points are independent.",
  "created_at": "2026-10-01 17:47:36",
  "updated_at": "2026-10-01 17:47:36"
}