{
  "id": 2228,
  "curve_key": "1036398793180921:-32712279933283560480781",
  "ainvs": [
    "1",
    "0",
    "1",
    "-21591641524603",
    "37861433308663623506"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.7235852005464,
  "faltings_height": 6.538736160616682,
  "conductor": "5605790190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "41",
    "157"
  ],
  "discriminant": "24957153525195079200004095854727539062500",
  "regulator": "4.139714852407061272719459484596063648616",
  "points": [
    [
      "2333305",
      "428705972"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=33; A=(3q-p)(p+q)^3=-2453125, B=-(p+3q)(p-q)^3=30896411. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 19:48:25",
  "updated_at": "2026-09-26 19:48:25"
}