{
  "id": 3396,
  "curve_key": "1075236546468254041:-1114951620828245402882157661",
  "ainvs": [
    "1",
    "0",
    "1",
    "-22400761384755293",
    "1290453262980776137939556"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 124.55721706347832,
  "faltings_height": 7.838733676413172,
  "conductor": "464963829330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "43",
    "59",
    "359"
  ],
  "discriminant": "9094461543021742283391523416554033430562500",
  "regulator": "110.49291936257169371379789012919448555392587",
  "points": [
    [
      "99122985",
      "209575228882"
    ],
    [
      "21965625225/256",
      "39880256329597/4096"
    ],
    [
      "45722877135/529",
      "3502852995584/12167"
    ]
  ],
  "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 = 157/177; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 464963829330, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:20:24",
  "updated_at": "2026-09-26 21:20:24"
}