{
  "id": 2507,
  "curve_key": "5581901521:356322791209319",
  "ainvs": [
    "1",
    "0",
    "0",
    "-116289615",
    "-412420328775"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 67.32838598898597,
  "faltings_height": 3.6034219585351934,
  "conductor": "274170",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "37"
  ],
  "discriminant": "27171794302813265625000000",
  "regulator": "4.658237581042813883072855951829358631663",
  "points": [
    [
      "-22305/4",
      "2024805/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=6; A=(3q-p)(p+q)^3=-81289, B=-(p+3q)(p-q)^3=-15625. 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 20:05:53",
  "updated_at": "2026-09-26 20:05:53"
}