{
  "id": 153,
  "curve_key": "59546361:-450133503885",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-1240549",
    "521297989"
  ],
  "rank_lower_bound": 9,
  "naive_height": 53.706797230758156,
  "faltings_height": 2.3725445185657126,
  "conductor": "616136865466771394",
  "bad_primes": [
    "2",
    "83",
    "14549",
    "255114981391"
  ],
  "discriminant": "4929094923734171152",
  "regulator": "102053.46086070287983607086017344691046650256242692048241",
  "points": [
    [
      "-10",
      "-23097"
    ],
    [
      "62",
      "21055"
    ],
    [
      "73",
      "20727"
    ],
    [
      "183",
      "17240"
    ],
    [
      "195",
      "16837"
    ],
    [
      "210",
      "16327"
    ],
    [
      "278",
      "13927"
    ],
    [
      "-286",
      "-29057"
    ],
    [
      "-410",
      "-30793"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Found by the ec-smallcond GPU integral-point search (Elkies-Watkins style large-rank/small-conductor sweep); rank >= 9 certified from 9 independent points via PARI/GP ellrank (returned rank exactly 9).",
  "created_at": "2026-06-24 21:09:07",
  "updated_at": "2026-07-01 22:52:29"
}