{
  "id": 2277,
  "curve_key": "1407748785430201:-52818336922323392160301",
  "ainvs": [
    "1",
    "0",
    "1",
    "-29328099696463",
    "61132331956828951406"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 104.64230465186735,
  "faltings_height": 6.338652018293852,
  "conductor": "2045228010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "41",
    "89",
    "157"
  ],
  "discriminant": "22448954150587084272520639297851562500",
  "regulator": "4.825882292316730680727865521432321982074",
  "points": [
    [
      "3134925",
      "13114162"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=41; A=(3q-p)(p+q)^3=53851, B=-(p+3q)(p-q)^3=37546875. 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 19:51:31",
  "updated_at": "2026-09-26 19:51:31"
}