{
  "id": 2616,
  "curve_key": "62089125626641:-176962695749874349561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1293523450555",
    "204817827102067025"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 95.27877593655661,
  "faltings_height": 5.9996666795849745,
  "conductor": "838767930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "31",
    "53"
  ],
  "discriminant": "120394374546008210967569390765625000000",
  "regulator": "16.4235684714226264964438624612986073094297",
  "points": [
    [
      "-1206310",
      "99626765"
    ],
    [
      "573875/4",
      "1191149515/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=22; A=(3q-p)(p+q)^3=-3545129, B=-(p+3q)(p-q)^3=5484375. 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 20:12:57",
  "updated_at": "2026-09-26 20:12:57"
}