{
  "id": 6178,
  "curve_key": "32927550742411785954081:-5934804609230092539284276291196465",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-685990640466912207377",
    "6868986816410030691695751537025"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 155.54579000639785,
  "faltings_height": 10.810377501958126,
  "conductor": "4611183920987854374283972944656606152532275998",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "152567",
    "9767749697",
    "1202122631955592866183495823"
  ],
  "discriminant": "277153811365506991014369371472342991972265109964043691252252672",
  "regulator": "40502905044105895411.5027022790282188857048388954134323457620087222879967",
  "points": [
    [
      "-3565807912929857/120409",
      "46008312357622292196700/41781923"
    ],
    [
      "-854558734918073/28561",
      "3764667787884528903188/4826809"
    ],
    [
      "-67342583129405/2401",
      "236620266419772723956/117649"
    ],
    [
      "-24189745337365/253009",
      "335130383348272138560140/127263527"
    ],
    [
      "-573570712001/25",
      "405646334748315172/125"
    ],
    [
      "535554875569/25",
      "176971048928188312/125"
    ],
    [
      "1143081337967/361",
      "14915109440400131708/6859"
    ],
    [
      "138809286401051/3481",
      "1345536527979218981084/205379"
    ],
    [
      "142817909590639/361",
      "1703115168641738154620/6859"
    ],
    [
      "172327598946439/10609",
      "119540516382484643564/1092727"
    ],
    [
      "516613501506143/32041",
      "8263025191609916/5735339"
    ],
    [
      "886236605174311/54289",
      "1825457758622833914580/12649337"
    ],
    [
      "1801767479174053/54289",
      "57492655939796088460450/12649337"
    ],
    [
      "2915178059021359/218089",
      "30166376971577986110076/101847563"
    ],
    [
      "3949182514516879/126025",
      "179759080740677348982332/44738875"
    ],
    [
      "85194132867523055/537289",
      "24546592624676536063106020/393832837"
    ],
    [
      "10254696380517660847/907877161",
      "20500413118847034521599407100/27355246738091"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,1,22,28,54,82,96,104,134,137: 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 17, proved: 17 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-30 14:40:33",
  "updated_at": "2026-10-30 14:40:33"
}