{
  "id": 2622,
  "curve_key": "30784434060961:-131482341235371101041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-641342376270",
    "152178582243888900"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 93.1740908715767,
  "faltings_height": 5.780097134454855,
  "conductor": "1282222110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "41",
    "53",
    "89"
  ],
  "discriminant": "6878604693658271310281584263744000000",
  "regulator": "15.1136218850792657057131402129444821640360",
  "points": [
    [
      "-3533265/4",
      "1377148365/8"
    ],
    [
      "-787620",
      "411144930"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=12; A=(3q-p)(p+q)^3=-6133969, B=-(p+3q)(p-q)^3=-4668625. 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 20:13:19",
  "updated_at": "2026-09-26 20:13:19"
}