{
  "id": 2535,
  "curve_key": "20741617521:-2987196727404681",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-432117032",
    "3457511648939"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 71.26622408133514,
  "faltings_height": 3.4749957275686385,
  "conductor": "155610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19"
  ],
  "discriminant": "2556079917020721000000",
  "regulator": "5.155600453551008925116870783784068414020",
  "points": [
    [
      "47871/4",
      "3371/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-9, q=10; A=(3q-p)(p+q)^3=39, B=-(p+3q)(p-q)^3=144039. 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 20:07:39",
  "updated_at": "2026-09-26 20:07:39"
}