{
  "id": 1153,
  "curve_key": "137920:-51209056",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2873",
    "58312"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "naive_height": 35.50328725769256,
  "faltings_height": 0.6790489329506069,
  "conductor": "310868",
  "bad_primes": [
    "2",
    "23",
    "31",
    "109"
  ],
  "discriminant": "657796688",
  "regulator": "8.3989161246526378713516746615191052021985075",
  "points": [
    [
      "31",
      "1"
    ],
    [
      "29",
      "15"
    ],
    [
      "43",
      "127"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 310868a1, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.310000-319999 . 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 21:37:46",
  "updated_at": "2026-09-23 21:37:46"
}