{
  "id": 2342,
  "curve_key": "15488810206489:-22579203870034278013",
  "ainvs": [
    "1",
    "0",
    "1",
    "-322683545969",
    "26133310922244176"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.11341687094139,
  "faltings_height": 5.6521115401655155,
  "conductor": "98888790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "37",
    "89"
  ],
  "discriminant": "1855321371443894857897157758717222500",
  "regulator": "3.386918205504221023364303093379456225976",
  "points": [
    [
      "-589929",
      "106072636"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-50, q=13; A=(3q-p)(p+q)^3=-4508117, B=-(p+3q)(p-q)^3=-2750517. 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 19:55:36",
  "updated_at": "2026-09-26 19:55:36"
}