{
  "id": 3395,
  "curve_key": "229926179681515881:-109869937502537504839207221",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-4790128743364914",
    "127164280714358001627348"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 119.92960408322824,
  "faltings_height": 7.81498655085495,
  "conductor": "17490168990",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "37",
    "101"
  ],
  "discriminant": "48544738631941129429564892966832301053924000000",
  "regulator": "97.707129290817376298092396520146374019840969",
  "points": [
    [
      "-63280988",
      "420603499494"
    ],
    [
      "2857296927/121",
      "219570109599039/1331"
    ],
    [
      "73548364548/1681",
      "2520469429880406/68921"
    ]
  ],
  "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 = -15/133; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 17490168990, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:20:14",
  "updated_at": "2026-09-26 21:20:14"
}