{
  "id": 2465,
  "curve_key": "195820187929:20498142749857667",
  "ainvs": [
    "1",
    "0",
    "1",
    "-4079587249",
    "-23725042222384"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 78.00138799972399,
  "faltings_height": 4.564865902981913,
  "conductor": "44021670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "59"
  ],
  "discriminant": "4102232736038225146765291476900",
  "regulator": "5.246230827077484881461788730617088889441",
  "points": [
    [
      "-183413/4",
      "65632219/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-2, q=19; A=(3q-p)(p+q)^3=289867, B=-(p+3q)(p-q)^3=509355. 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 20:03:15",
  "updated_at": "2026-09-26 20:03:15"
}