{
  "id": 2333,
  "curve_key": "27503185878961:-143728862631740888041",
  "ainvs": [
    "1",
    "0",
    "0",
    "-572983039145",
    "166352802519632025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 92.835968892105,
  "faltings_height": 5.557889147792261,
  "conductor": "206308410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "43",
    "67"
  ],
  "discriminant": "84558939161924101152830770449000000",
  "regulator": "6.327653640866345186328553439485940092016",
  "points": [
    [
      "-2669645/4",
      "4014476675/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=6; A=(3q-p)(p+q)^3=-5326969, B=-(p+3q)(p-q)^3=-5157625. 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 19:55:02",
  "updated_at": "2026-09-26 19:55:02"
}