{
  "id": 2428,
  "curve_key": "1260362454169:-1405923044918040253",
  "ainvs": [
    "1",
    "0",
    "1",
    "-26257551129",
    "1627223558303656"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 83.5872613726921,
  "faltings_height": 4.811615965472887,
  "conductor": "52052970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "29",
    "47",
    "67"
  ],
  "discriminant": "14747213612354834443742767844100",
  "regulator": "10.05450662232241969049359423145334636133",
  "points": [
    [
      "-72487",
      "56158278"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=19; A=(3q-p)(p+q)^3=48843, B=-(p+3q)(p-q)^3=1146283. 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 20:01:00",
  "updated_at": "2026-09-26 20:01:00"
}