{
  "id": 2643,
  "curve_key": "1854273001441:-2109365036653415761",
  "ainvs": [
    "1",
    "0",
    "0",
    "-38630687530",
    "2441391499124900"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.74554146660053,
  "faltings_height": 5.061023892328608,
  "conductor": "25526670",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "29",
    "37",
    "61"
  ],
  "discriminant": "1114686688288583278701121536000000",
  "regulator": "10.9577057552565496430880654095952579932749",
  "points": [
    [
      "-214540",
      "29339270"
    ],
    [
      "-192940",
      "52177670"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=8; A=(3q-p)(p+q)^3=-1487729, B=-(p+3q)(p-q)^3=-1184625. 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 20:14:58",
  "updated_at": "2026-09-26 20:14:58"
}