{
  "id": 2576,
  "curve_key": "32980249:100241285507",
  "ainvs": [
    "1",
    "0",
    "1",
    "-687089",
    "-116077264"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 51.93425827529264,
  "faltings_height": 2.376383438900529,
  "conductor": "51870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19"
  ],
  "discriminant": "14944558319037792900",
  "regulator": "2.503003782291380187994058816762672096120",
  "points": [
    [
      "-684",
      "6172"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=3; A=(3q-p)(p+q)^3=-6517, B=-(p+3q)(p-q)^3=-2197. 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 20:10:22",
  "updated_at": "2026-09-26 20:10:22"
}