{
  "id": 2343,
  "curve_key": "14996019689721:-28404089515714995981",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-312417076869",
    "32875181710420833"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.01641778339865,
  "faltings_height": 5.636506708911202,
  "conductor": "32930370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "29",
    "31",
    "37"
  ],
  "discriminant": "1484676911001742579391069540039062500",
  "regulator": "4.781664106779315518806568895491016013929",
  "points": [
    [
      "-2040297/4",
      "1953809907/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-6, q=31; A=(3q-p)(p+q)^3=1546875, B=-(p+3q)(p-q)^3=4406811. 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 19:55:39",
  "updated_at": "2026-09-26 19:55:39"
}