{
  "id": 4337,
  "curve_key": "1659065344:-257086760187232",
  "ainvs": [
    "0",
    "1",
    "0",
    "-34563861",
    "297542599300"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 66.36086946426167,
  "faltings_height": 3.5857836710158293,
  "conductor": "31146261647020",
  "bad_primes": [
    "2",
    "5",
    "13",
    "17",
    "41",
    "59",
    "223",
    "13063"
  ],
  "discriminant": "-35605919287133726924252080",
  "regulator": "1763.8282505896928968195938467401804905575726850558",
  "points": [
    [
      "-7329",
      "396539"
    ],
    [
      "1069539",
      "-1106085331"
    ],
    [
      "78575",
      "21970715"
    ],
    [
      "-59825/9",
      "13050505/27"
    ],
    [
      "16389",
      "-2033081"
    ],
    [
      "126129",
      "44749081"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "BASE torsion/torsion_Z3.tsv.gz:491 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 10:05:22",
  "updated_at": "2026-10-17 10:05:22"
}