{
  "id": 2413,
  "curve_key": "2171237047281:-1375103009483733321",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-45234105152",
    "1591565717650979"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.21895456677615,
  "faltings_height": 5.157510749005021,
  "conductor": "5462730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "29"
  ],
  "discriminant": "4829218792354177360706793681000000",
  "regulator": "4.889683961112287740367168180313598288464",
  "points": [
    [
      "-228263",
      "4949881"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=10; A=(3q-p)(p+q)^3=-1682841, B=-(p+3q)(p-q)^3=-1058841. 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 20:00:04",
  "updated_at": "2026-09-26 20:00:04"
}