{
  "id": 1249,
  "curve_key": "1065529:-423015533",
  "ainvs": [
    "1",
    "1",
    "0",
    "-22198",
    "480352"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2
  ],
  "naive_height": 41.636945842257944,
  "faltings_height": 1.528322248676518,
  "conductor": "1364469990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "59",
    "3121"
  ],
  "discriminant": "596532634928100",
  "regulator": "27.1736722324320507914593821399755786075949029674",
  "points": [
    [
      "-159",
      "227"
    ],
    [
      "-149",
      "787"
    ],
    [
      "-54",
      "1262"
    ],
    [
      "726",
      "18812"
    ],
    [
      "6862",
      "564916"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Found by a conductor-oriented search based on Thomas J. Kretschmer’s Construction of Elliptic Curves with Large Rank (Math. Comp. 46 (1986), 627–635). I searched curves of the form \\(y^2=x^3+ax^2+bx\\) with rational 2-torsion, taking \\(b=2^{e_2}3^{e_3}pqr\\) and looking for values of \\(a\\) for which enough of Kretschmer’s conditions \\(b_1+a+b_2=\\square\\) are satisfied to force rank at least 5. Candidates were then tested for exact rank and conductor. This produced \\(y^2=x^3+1637x^2+538080x\\), whose minimal model has ainvs \\([1,1,0,-22198,480352]\\), exact rank 5, torsion \\(\\mathbf Z/2\\mathbf Z\\), and conductor \\(1364469990\\), independently confirmed in Magma.",
  "created_at": "2026-09-24 16:18:28",
  "updated_at": "2026-09-24 16:18:28"
}