{
  "id": 3381,
  "curve_key": "21830675450120881:-3177522587119720173039721",
  "ainvs": [
    "1",
    "0",
    "0",
    "-454805738544185",
    "3677688141636234951225"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 112.86627751909349,
  "faltings_height": 7.288251300205524,
  "conductor": "265642379310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "97",
    "167",
    "229"
  ],
  "discriminant": "177881007094520248546025436567964487961000000",
  "regulator": "132.64996868989984666901851282524895882227495",
  "points": [
    [
      "37527670",
      "198629374315"
    ],
    [
      "177030445/16",
      "13905513835/64"
    ],
    [
      "4421258422/841",
      "922860057828023/24389"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/6ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=(10-2t)/(t^2-9), b=c+c^2, at t = 68/33; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 265642379310, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:17:54",
  "updated_at": "2026-09-26 21:17:54"
}