{
  "id": 6448,
  "curve_key": "10877124778857514130401:-1111655700179973384494599543755601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-226606766226198211050",
    "1286638541856085297831381102500"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 152.22284667818715,
  "faltings_height": 10.581495792358426,
  "conductor": "594031745999888841588209639676759504494404410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "53",
    "179",
    "178469",
    "9239887",
    "24203837090149",
    "52293273415723"
  ],
  "discriminant": "29580027970070802426245383657148505349573710750202296000000000",
  "regulator": "17365458542869.3058067879202587419238943525085984735958563148616489156066",
  "points": [
    [
      "1171022451900/121",
      "-3865049063173350/1331"
    ],
    [
      "30627178819900/9",
      "-169494795365705871350/27"
    ],
    [
      "95025112058350/9801",
      "-30275567400150136450/970299"
    ],
    [
      "2491822620084/25",
      "-3890939782364058162/125"
    ],
    [
      "41327457676950/5929",
      "-97668193049249706750/456533"
    ],
    [
      "4078023623700/1681",
      "-59734313544543064650/68921"
    ],
    [
      "7281948247860/361",
      "15219047399183976450/6859"
    ],
    [
      "159745537158900/2809",
      "1954317901589064759150/148877"
    ],
    [
      "127037931661165/1296",
      "1415860515231431723675/46656"
    ],
    [
      "9776035830",
      "75008373370320"
    ],
    [
      "-1612572900",
      "-1283691193921050"
    ],
    [
      "135209184004/9",
      "-30463373553959086/27"
    ],
    [
      "5319042816900/529",
      "1911779068498996650/12167"
    ],
    [
      "9862291860",
      "105020439259590"
    ],
    [
      "-5128857900",
      "1521172146538950"
    ],
    [
      "232137344262460/23409",
      "433589230372806686350/3581577"
    ],
    [
      "-436921878983025/217156",
      "133271266891275462009825/101194696"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,22,33,50,77,82,95,106,120,143: 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); for the sets with S >= 31, or S >= 30 and one bad prime in that range, or S >= 29 and two or more bad primes, rational points were found by a point search on the quartic y^2 = r(x), and the curves were screened by conductor and by a GRH explicit-formula upper bound on the rank. Rank 17, proved: the 17 listed points come from the point search and are independent, and the 2-descent upper bound (ellrank) is 17. Torsion trivial.",
  "created_at": "2026-11-03 14:23:48",
  "updated_at": "2026-11-03 14:23:48"
}