{
  "id": 2468,
  "curve_key": "327381828841:-187036507220863861",
  "ainvs": [
    "1",
    "0",
    "1",
    "-6820454768",
    "216476870541806"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 79.5431789968237,
  "faltings_height": 4.417257953162006,
  "conductor": "4576530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "31",
    "37"
  ],
  "discriminant": "61201836746231231285156250000",
  "regulator": "8.124954917217048157333758440317236336372",
  "points": [
    [
      "31277",
      "5793879"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=3; A=(3q-p)(p+q)^3=-578125, B=-(p+3q)(p-q)^3=-566029. 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 20:03:26",
  "updated_at": "2026-09-26 20:03:26"
}