{
  "id": 6098,
  "curve_key": "471626691212675999056:-10134010260336097629075074599360",
  "ainvs": [
    "0",
    "1",
    "0",
    "-9825556066930749980",
    "11729178538780483196526641904"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 142.80815831429268,
  "faltings_height": 9.76828536178711,
  "conductor": "1581722370777087577044826670736769612479144504",
  "bad_primes": [
    "2",
    "3",
    "11",
    "107",
    "1427843",
    "550547449",
    "71230721124850608298359839"
  ],
  "discriminant": "1276955815818982797094188612377389647696308997173989846272",
  "regulator": "39754261530517.0192672605795920528105237220773637026219118307065887714131",
  "points": [
    [
      "-3612394184",
      "9133088968476"
    ],
    [
      "-3034842638",
      "116603925456546"
    ],
    [
      "-1027363208",
      "144011239122564"
    ],
    [
      "-698055086",
      "135084451406718"
    ],
    [
      "-141809594",
      "114541192896174"
    ],
    [
      "1593196690",
      "10913641487298"
    ],
    [
      "1640286106",
      "5070342790326"
    ],
    [
      "1655497654",
      "412781378658"
    ],
    [
      "2006023555",
      "9559404239352"
    ],
    [
      "2047774099",
      "13991130546228"
    ],
    [
      "2061958324",
      "15364314566172"
    ],
    [
      "2323096762",
      "37956552415254"
    ],
    [
      "2366316202",
      "41579813490534"
    ],
    [
      "2519745214",
      "54492524095482"
    ],
    [
      "3754867828",
      "166659885309060"
    ],
    [
      "7203588466",
      "561031436426274"
    ],
    [
      "22202497225/16",
      "1772166555319347/64"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,16,38,43,51,53,61,76,102,120: 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": "2026-10-29 02:28:32",
  "updated_at": "2026-10-29 02:28:32"
}