{
  "id": 1912,
  "curve_key": "190558144:-2473663228928",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-3969961",
    "2864359465"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 57.196403771427924,
  "faltings_height": 2.714468076684121,
  "conductor": "21524842560",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "31",
    "41",
    "59"
  ],
  "discriminant": "463318847232787353600",
  "regulator": "90.7101828331645530012470143478129818835379076307",
  "points": [
    [
      "-2272",
      "12285"
    ],
    [
      "-2192",
      "32085"
    ],
    [
      "-1991",
      "53592"
    ],
    [
      "-1752",
      "66625"
    ],
    [
      "-1517",
      "73440"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Found on 2026-09-25 the family y^2 = u(u+a)(u+b), with a = 460, b = 3658 and x = u+1373.\r\n\r\nThe five submitted points were verified to be independent modulo torsion by exact full 2-descent: the square-class matrix has rank 7, including two torsion rows of rank 2. An additional certificate using quadratic characters at good primes gives the same ranks. The torsion subgroup is exactly Z/2Z x Z/2Z, verified using good-prime reduction counts.\r\n\r\nThis proves rank >= 5. Comparison data were obtained from the ICARM Elliptic Curve Rank Leaderboard, supported by NSF Grant DMS 2425401.",
  "created_at": "2026-09-25 18:24:54",
  "updated_at": "2026-09-25 18:24:54"
}