{
  "id": 2399,
  "curve_key": "3165735645081:4173957126831926979",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-65952825939",
    "-4830952408589727"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 86.35021972746578,
  "faltings_height": 5.217192751462904,
  "conductor": "2612610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29"
  ],
  "discriminant": "8278189545197209746755782197562500",
  "regulator": "7.503463014608901282331618912790419339742",
  "points": [
    [
      "-90348",
      "19800129"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-42, q=13; A=(3q-p)(p+q)^3=-1975509, B=-(p+3q)(p-q)^3=-499125. 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 19:59:10",
  "updated_at": "2026-09-26 19:59:10"
}