{
  "id": 2510,
  "curve_key": "3942359001:-2962619913501",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-82132479",
    "3449491353"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 66.28513533691951,
  "faltings_height": 3.5919929877276915,
  "conductor": "296010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23"
  ],
  "discriminant": "35453780808504447380062500",
  "regulator": "3.487515320223940045285854548901448724502",
  "points": [
    [
      "-8261",
      "347831"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-18, q=5; A=(3q-p)(p+q)^3=-72501, B=-(p+3q)(p-q)^3=-36501. 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 20:06:05",
  "updated_at": "2026-09-26 20:06:05"
}