{
  "id": 3382,
  "curve_key": "72072723220943641:-19348616388892852826760061",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1501515067102993",
    "22394231806462694439056"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 116.44935614673031,
  "faltings_height": 7.343506104199714,
  "conductor": "24657882990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "61",
    "109",
    "257"
  ],
  "discriminant": "6468810320606308281532898319099228057562500",
  "regulator": "153.32498789762503080526497485266912546580928",
  "points": [
    [
      "22577260",
      "1570757807"
    ],
    [
      "60985793905/256",
      "14872204020005327/4096"
    ],
    [
      "99747077365/4489",
      "326870085411866/300763"
    ]
  ],
  "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 = 187/135; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 24657882990, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:18:05",
  "updated_at": "2026-09-26 21:18:05"
}