{
  "id": 2648,
  "curve_key": "2811187847521:-4709857955180449681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-58566413490",
    "5451219604628100"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.99388469447103,
  "faltings_height": 4.929310960832699,
  "conductor": "103032930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "47",
    "73"
  ],
  "discriminant": "19345501566654581752289856000000",
  "regulator": "5.06104121346854426426900534466768505798967",
  "points": [
    [
      "-272220",
      "35088510"
    ],
    [
      "-235428",
      "78797406"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=20; A=(3q-p)(p+q)^3=25039, B=-(p+3q)(p-q)^3=1689039. 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 20:15:20",
  "updated_at": "2026-09-26 20:15:20"
}