{
  "id": 1182,
  "curve_key": "6704477473:-548968469763889",
  "ainvs": [
    "1",
    "0",
    "0",
    "-139676614",
    "635368533620"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8
  ],
  "naive_height": 67.87812425908868,
  "faltings_height": 3.1140666983879197,
  "conductor": "253506",
  "bad_primes": [
    "2",
    "3",
    "11",
    "23",
    "167"
  ],
  "discriminant": "2050829383126824432",
  "regulator": "30.8553159876079266358067789058809713768294",
  "points": [
    [
      "7130",
      "40640"
    ],
    [
      "8306",
      "215528"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 253506bg3, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.250000-259999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.",
  "created_at": "2026-09-23 21:38:37",
  "updated_at": "2026-09-23 21:38:37"
}