{
  "id": 4335,
  "curve_key": "31366390057:-5554850136513301",
  "ainvs": [
    "1",
    "0",
    "1",
    "-653466460",
    "6429170239500"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 72.50700832873243,
  "faltings_height": 3.720237410812481,
  "conductor": "21820427847974",
  "bad_primes": [
    "2",
    "7",
    "19",
    "43",
    "61",
    "103",
    "113",
    "2687"
  ],
  "discriminant": "2011664174461092729139814",
  "regulator": "20369.774469792387005424036504668239579169622460413",
  "points": [
    [
      "3659249/256",
      "-420049137/4096"
    ],
    [
      "59547/4",
      "-212553/8"
    ],
    [
      "139796/25",
      "214343091/125"
    ],
    [
      "4517012/841",
      "42697729356/24389"
    ],
    [
      "10677658/729",
      "-414845261/19683"
    ],
    [
      "241426/9",
      "-77692669/27"
    ]
  ],
  "submitter": "Volkan Dagli",
  "history": [],
  "commentary": "BASE torsion/torsion_Z3.tsv.gz:487 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.",
  "created_at": "2026-10-17 10:05:19",
  "updated_at": "2026-10-17 10:05:19"
}