{
  "id": 3756,
  "curve_key": "14330560:-51836168800",
  "ainvs": [
    "0",
    "1",
    "0",
    "-298553",
    "59896048"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "naive_height": 49.43371463368903,
  "faltings_height": 2.053275178639923,
  "conductor": "341505273100",
  "bad_primes": [
    "2",
    "5",
    "29",
    "61",
    "89",
    "109",
    "199"
  ],
  "discriminant": "148151817576242000",
  "regulator": "601.52942782586698096119920737325833409621744709412",
  "points": [
    [
      "-627",
      "995"
    ],
    [
      "-613",
      "3597"
    ],
    [
      "-177",
      "10355"
    ],
    [
      "913",
      "23435"
    ],
    [
      "1363",
      "46765"
    ],
    [
      "477/4",
      "40795/8"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found 2026-10-01 in a discriminant-first search for elliptic curves over Q with rational 2-torsion. The search used the visible-2-torsion family y^2 = x^3 + A*x^2 + B*x and a Kretschmer-type four-square pattern with B = 5*109*199 = 108455 and A = 1105. PARI/GP 2.17.4 on the global minimal model gives ellrank bounds [6,6], torsion Z/2Z, conductor 341505273100, and minimal discriminant 148151817576242000. The six submitted points are the independent generators returned by ellrank(E,1).",
  "created_at": "2026-10-01 14:38:31",
  "updated_at": "2026-10-01 14:38:31"
}