{
  "id": 2506,
  "curve_key": "12656886001:-1423556522829001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-263685125",
    "1647612890625"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 69.7844017557645,
  "faltings_height": 3.5426159621621958,
  "conductor": "3038070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "37"
  ],
  "discriminant": "624419211866828049000000",
  "regulator": "4.552000068653776600231922546416867224788",
  "points": [
    [
      "12975/4",
      "7259625/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=10; A=(3q-p)(p+q)^3=999, B=-(p+3q)(p-q)^3=112999. 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 20:05:50",
  "updated_at": "2026-09-26 20:05:50"
}