{
  "id": 2400,
  "curve_key": "3319172518561:-5871574660068739441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-69149427470",
    "6795798242256900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 86.49220987918157,
  "faltings_height": 5.121093228696093,
  "conductor": "16546530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "29"
  ],
  "discriminant": "1210430171469135434744070144000000",
  "regulator": "2.171614594174883834648948588518253889284",
  "points": [
    [
      "-291260",
      "47347330"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=16; A=(3q-p)(p+q)^3=-169169, B=-(p+3q)(p-q)^3=1731375. 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 19:59:14",
  "updated_at": "2026-09-26 19:59:14"
}