{
  "id": 3757,
  "curve_key": "2070496:-11502559360",
  "ainvs": [
    "0",
    "1",
    "0",
    "-43135",
    "13298769"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "naive_height": 46.33167080119568,
  "faltings_height": 1.9167735781897863,
  "conductor": "323366397056",
  "bad_primes": [
    "2",
    "17",
    "73",
    "89",
    "257"
  ],
  "discriminant": "-71430990376876288",
  "regulator": "774.36917814722390015807505845567319802449820904172",
  "points": [
    [
      "-224",
      "3431"
    ],
    [
      "-208",
      "3649"
    ],
    [
      "-161",
      "4012"
    ],
    [
      "-119",
      "4094"
    ],
    [
      "287",
      "4964"
    ],
    [
      "53/4",
      "28543/8"
    ]
  ],
  "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 together with Kretschmer-type divisor-square conditions. The source model is y^2 = x^3 - 890*x^2 + 220898*x, with 220898 = 2*17*73*89. PARI/GP 2.17.4 gives exact ellrank bounds [6,6], torsion Z/2Z, conductor 323366397056, and minimal discriminant -71430990376876288. ",
  "created_at": "2026-10-01 15:56:45",
  "updated_at": "2026-10-01 15:56:45"
}