{
  "id": 2653,
  "curve_key": "2975044059001:-5130965303037463501",
  "ainvs": [
    "1",
    "0",
    "1",
    "-61980084563",
    "5938612083878906"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 86.16383989369415,
  "faltings_height": 4.8741786731432954,
  "conductor": "154392810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "29",
    "73"
  ],
  "discriminant": "2878646086865277774574520062500",
  "regulator": "7.66969307670939264978926766790812977553034",
  "points": [
    [
      "-899925/4",
      "738255371/8"
    ],
    [
      "-192660",
      "103675162"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=17; A=(3q-p)(p+q)^3=-9125, B=-(p+3q)(p-q)^3=1720251. 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 20:15:41",
  "updated_at": "2026-09-26 20:15:41"
}