{
  "id": 2612,
  "curve_key": "116132975386849:-1243016066642529411793",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2419436987226",
    "1438675801438734180"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.15727097009373,
  "faltings_height": 5.945008233095581,
  "conductor": "1171313430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "59",
    "67",
    "83"
  ],
  "discriminant": "12257618246531867402252221227525734400",
  "regulator": "42.8342722789392858618756842629742777544752",
  "points": [
    [
      "-1707820",
      "768660950"
    ],
    [
      "-1392946",
      "1451933960"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-59, q=8; A=(3q-p)(p+q)^3=-11010033, B=-(p+3q)(p-q)^3=-10526705. 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 20:12:42",
  "updated_at": "2026-09-26 20:12:42"
}