{
  "id": 3714,
  "curve_key": "5093072010793380507201:-363441218719736771256380812200801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-106105666891528760567",
    "420649558729925457528878500559"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 149.94650441954275,
  "faltings_height": 10.18494895351623,
  "conductor": "85197380776083810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "337",
    "373",
    "3253",
    "4813"
  ],
  "discriminant": "12513634157431680639757513144354533613753995264000000000000",
  "regulator": "76148.562460842440576891967019646897425395722140393",
  "points": [
    [
      "237814467",
      "628831771092766"
    ],
    [
      "6041793597",
      "11232727163416"
    ],
    [
      "7113520323",
      "160695900034078"
    ],
    [
      "-288880348077/49",
      "314606274023391538/343"
    ],
    [
      "783703901383/49",
      "575477350569381238/343"
    ],
    [
      "34428032598843/5929",
      "8096670443160492278/456533"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -274449/134800 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 01:48:24",
  "updated_at": "2026-09-30 01:48:24"
}