{
  "id": 2305,
  "curve_key": "106694647313809:-1101265390492061958073",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2222805152371",
    "1274612535243160865"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 96.90297632166501,
  "faltings_height": 5.837847226279482,
  "conductor": "1047776730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "37",
    "41"
  ],
  "discriminant": "1041373058455277920536895651754433600",
  "regulator": "3.660239142261719528824207343111142444313",
  "points": [
    [
      "-1681006",
      "511728881"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=26; A=(3q-p)(p+q)^3=-153065, B=-(p+3q)(p-q)^3=10251927. 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 19:53:19",
  "updated_at": "2026-09-26 19:53:19"
}