{
  "id": 6467,
  "curve_key": "4414063706612428245822081:-8952499751948424997821181162675058625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-91959660554425588454627",
    "10361689527741074403357566076135715"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 170.24051391732098,
  "faltings_height": 12.108507302641744,
  "conductor": "8845203848788098026820445114527786174959429151384172062",
  "bad_primes": [
    "2",
    "3",
    "17",
    "31",
    "47",
    "1303",
    "5113",
    "208433",
    "303978118223363606172009310463062199"
  ],
  "discriminant": "3388994127650467866726326437178360513046946849552588945269282114895872",
  "regulator": "1032205263562509811.096850127138854191656998309341196291382507158600602085905",
  "points": [
    [
      "4925556853351/36",
      "-3988495411852541683/216"
    ],
    [
      "174477101258425",
      "-2304660810159862633816"
    ],
    [
      "24151699327211/169",
      "-25850188952848275430/2197"
    ],
    [
      "204807933681517/3721",
      "16782590234701652321030/226981"
    ],
    [
      "-64391137493/4",
      "870415680283555537/8"
    ],
    [
      "-197001266073959/576",
      "-587483439992168604871/13824"
    ],
    [
      "-1758309099083255/5329",
      "-26903682509109249679762/389017"
    ],
    [
      "4790775447595/4",
      "10176922165303524865/8"
    ],
    [
      "461656532072467/361",
      "9661580058506285140838/6859"
    ],
    [
      "-277956617765",
      "120198268891533170"
    ],
    [
      "-275873735825",
      "121388812577141390"
    ],
    [
      "-111259342133",
      "138621198988317122"
    ],
    [
      "203824261987",
      "9263911185350762"
    ],
    [
      "232859003419",
      "39679120199138930"
    ],
    [
      "254091013531",
      "58311552514445042"
    ],
    [
      "436001149741",
      "230541933202412996"
    ],
    [
      "500261444123",
      "299255497645657714"
    ],
    [
      "-175370207942989/841",
      "3489447290843599867834/24389"
    ],
    [
      "51390035839019/625",
      "905210665760157366722/15625"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,18,39,61,62,72,73,94,95,116: with p(x) = prod (x - a_i), write p = q^2 - r with q a monic quintic and deg r <= 4; the genus-one curve y^2 = r(x) carries the ten points (a_i, q(a_i)), and the curve submitted is the minimal Weierstrass model of its Jacobian. Found by enumerating integer ten-root sets 0 = a_1 < ... < a_10 and scoring each by S = sum of -a_p log(p)/p over the good primes 5 <= p <= 199 (with early abort on low partial sums); the sets with S >= 31, or S >= 30 and one bad prime in that range, or S >= 29 and two or more bad primes, were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 19, proved: 19 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-11-04 02:10:08",
  "updated_at": "2026-11-04 02:10:08"
}