{
  "id": 2530,
  "curve_key": "1710406369:-70651812518353",
  "ainvs": [
    "1",
    "0",
    "0",
    "-35633466",
    "81769961700"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 63.77999046575546,
  "faltings_height": 3.095425620213034,
  "conductor": "214890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "29"
  ],
  "discriminant": "7001172374869514649600",
  "regulator": "2.111921546454282006682368188730322760303",
  "points": [
    [
      "-3564",
      "406134"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=3; A=(3q-p)(p+q)^3=-667888, B=-(p+3q)(p-q)^3=-655360. 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 20:07:20",
  "updated_at": "2026-09-26 20:07:20"
}