{
  "id": 3710,
  "curve_key": "5197113627276347344:-11847952717585323075780148288",
  "ainvs": [
    "0",
    "1",
    "0",
    "-108273200568257236",
    "13712908201854908926067204"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 129.2839052210798,
  "faltings_height": 8.247635776369203,
  "conductor": "21175657519450980",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "29",
    "59",
    "1979",
    "2621"
  ],
  "discriminant": "2192346096586826707645695580418704252987994880",
  "regulator": "21715.392174460056260772206150107101179384997951897",
  "points": [
    [
      "165107612",
      "580601914662"
    ],
    [
      "189405620",
      "13614868722"
    ],
    [
      "189753092",
      "5314797762"
    ],
    [
      "189864071",
      "2648833320"
    ],
    [
      "4739594404/25",
      "1170278148858/125"
    ],
    [
      "177737440856/625",
      "38018992336662246/15625"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -47818/767 of the universal curve with a 6-torsion point, y^2 + txy + (t+2)y = x^3 (as searched in arXiv:2003.00077, Sec. 13), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:47:40",
  "updated_at": "2026-09-30 01:47:40"
}