{
  "id": 80,
  "curve_key": "19303536:-83195714520",
  "ainvs": [
    "0",
    "0",
    "1",
    "-402157",
    "96291336"
  ],
  "rank_lower_bound": 9,
  "naive_height": 50.327396548587,
  "faltings_height": 2.087850183987795,
  "conductor": "157107745029925477",
  "bad_primes": [
    "157107745029925477"
  ],
  "discriminant": "157107745029925477",
  "regulator": "1253079.4942741755784427259681451604931159440062484019892",
  "points": [
    [
      "-9",
      "9995"
    ],
    [
      "16",
      "9479"
    ],
    [
      "46",
      "8825"
    ],
    [
      "61",
      "8484"
    ],
    [
      "74",
      "8181"
    ],
    [
      "-76",
      "11243"
    ],
    [
      "102",
      "7505"
    ],
    [
      "108",
      "7356"
    ],
    [
      "-113",
      "11844"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=9: [0,0,1,-402157,96291336], |Delta|=157107745029925477, I=131. The submitted integral points give the rank >= 9 witness checked by the site.",
  "created_at": "2026-06-02 18:44:32",
  "updated_at": "2026-07-01 22:51:30"
}