{
  "id": 2421,
  "curve_key": "1624701787801:1995465647833503299",
  "ainvs": [
    "1",
    "0",
    "1",
    "-33847953913",
    "-2309569542692344"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.34903619900967,
  "faltings_height": 4.953277722429156,
  "conductor": "9699690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19"
  ],
  "discriminant": "177529228623962620992500976562500",
  "regulator": "5.000094929790965463161921139808691686372",
  "points": [
    [
      "-379925/4",
      "56085571/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=13; A=(3q-p)(p+q)^3=-1203125, B=-(p+3q)(p-q)^3=132651. 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 20:00:33",
  "updated_at": "2026-09-26 20:00:33"
}