{
  "id": 3707,
  "curve_key": "341470738794193508014019521:-6310227455868996645383169427482727793569",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7113973724879031416958740",
    "7303503999847782915827520992153595792"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    5
  ],
  "naive_height": 183.28598069912027,
  "faltings_height": 12.936806910762842,
  "conductor": "177700463308819182300270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "19",
    "37",
    "41",
    "43",
    "331",
    "250091",
    "261241"
  ],
  "discriminant": "-1567601625608890762147360135731913761034693551969414758912111158886400000",
  "regulator": "1214341.127162800473958601269035158014532898289053887",
  "points": [
    [
      "809102756584",
      "1441264720297380268"
    ],
    [
      "1541932846264",
      "16349386579680028"
    ],
    [
      "-2013497389645466/841",
      "79450015774409150841482/24389"
    ],
    [
      "113850500896744/81",
      "207742533465272411852/729"
    ],
    [
      "1435301417006824/841",
      "8905772098481890034012/24389"
    ],
    [
      "3713893654348312/2401",
      "2547056226346889279980/117649"
    ],
    [
      "10489000725737896/9409",
      "794785738361285831394604/912673"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 3891105/152048 of the universal curve with a 5-torsion point, y^2 + (t+1)xy + ty = x^3 + tx^2 (as searched in arXiv:2003.00077, Sec. 12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:47:06",
  "updated_at": "2026-09-30 01:47:06"
}