{
  "id": 2563,
  "curve_key": "50256001:200305759679",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1047000",
    "-231922620"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 53.19792156197606,
  "faltings_height": 2.4786586555256984,
  "conductor": "4290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13"
  ],
  "discriminant": "50235797102795981820",
  "regulator": "6.435615726674132077395428383653496993759",
  "points": [
    [
      "2112",
      "82482"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "3-isogenous to S-1055; original source https://elliptic-rank.icarm.cloud/curve/1055. Rational 3-torsion kernel with x=420; independent point witnesses transported by explicit Vélu map.",
  "created_at": "2026-09-26 20:09:27",
  "updated_at": "2026-09-26 20:09:27"
}