{
  "id": 6476,
  "curve_key": "800134027310800:-23359872295322021240000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-16669458902308",
    "27036894787183084612"
  ],
  "rank_lower_bound": 15,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 103.0106132880204,
  "faltings_height": 6.500460462202123,
  "conductor": "322398322749244260811230752852826600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "21247",
    "20054201",
    "1261068106038586980913"
  ],
  "discriminant": "-19343899364954655648673845171169596000000",
  "regulator": "892629286071.47890220853646057883493408371901623000430649207432530434",
  "points": [
    [
      "95446624/9",
      "-871985990906/27"
    ],
    [
      "316685617",
      "-5635164489300"
    ],
    [
      "-7634839823/1936",
      "477663513998625/85184"
    ],
    [
      "-70373852/169",
      "12792894118350/2197"
    ],
    [
      "3618588213/2209",
      "210895763440750/103823"
    ],
    [
      "155083188/289",
      "-20986191438650/4913"
    ],
    [
      "1381992157/841",
      "-49274416289250/24389"
    ],
    [
      "145792558/49",
      "666815056200/343"
    ],
    [
      "34711847248/11449",
      "2559984062758950/1225043"
    ],
    [
      "-4646348",
      "2044765350"
    ],
    [
      "-4300608",
      "4380063250"
    ],
    [
      "-4188708",
      "4834081150"
    ],
    [
      "2111892",
      "1118935750"
    ],
    [
      "10767792",
      "33106175650"
    ],
    [
      "13417057",
      "47102925600"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,3,22,26,47,68,87,105,107,121: 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 15, proved: 15 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-11-04 02:11:16",
  "updated_at": "2026-11-04 02:11:16"
}