{
  "id": 135,
  "curve_key": "51656857:-428648563261",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1076185",
    "496031340"
  ],
  "rank_lower_bound": 9,
  "naive_height": 53.5678064405781,
  "faltings_height": 2.4507827662879853,
  "conductor": "77211251506212554",
  "bad_primes": [
    "2",
    "43",
    "897805250072239"
  ],
  "discriminant": "-26560670518137118576",
  "regulator": "53538.096568535612150394273481249423219180410009474496562",
  "points": [
    [
      "679",
      "8518"
    ],
    [
      "335",
      "12990"
    ],
    [
      "1023",
      "21074"
    ],
    [
      "-525",
      "30534"
    ],
    [
      "-1041",
      "22622"
    ],
    [
      "-1213",
      "4734"
    ],
    [
      "120",
      "19139"
    ],
    [
      "34",
      "21418"
    ],
    [
      "1668",
      "56979"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "From the tables of Elkies-Watkins 2004, 'Elliptic curves of large rank and small conductor' (ANTS-VI, arXiv:math/0403374): a low-conductor / low-discriminant curve of this rank that was absent from the leaderboard. Witness: a maximal independent set of rational points (Neron-Tate height pairing).",
  "created_at": "2026-06-24 00:08:43",
  "updated_at": "2026-07-01 22:52:28"
}