{
  "id": 6023,
  "curve_key": "341521615955908425:-172938964115142225844093125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-7115033665748092",
    "200160839874987844497316"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 121.11656210702219,
  "faltings_height": 8.081411126065948,
  "conductor": "1913974163683850342150265853980708936255950",
  "bad_primes": [
    "2",
    "5",
    "7",
    "86017",
    "5090675449571",
    "12488443836690756079331"
  ],
  "discriminant": "5744314958756155839378485394259602694938169937500",
  "regulator": "176918595405978.1798358622683071420983208153145407316612467420045630785",
  "points": [
    [
      "-95923191",
      "6642114983"
    ],
    [
      "-84729456",
      "441329304178"
    ],
    [
      "-83215216",
      "464792600958"
    ],
    [
      "-51451456",
      "655796030778"
    ],
    [
      "-30751216",
      "624416912958"
    ],
    [
      "12057094",
      "340768078728"
    ],
    [
      "62771184",
      "29534149358"
    ],
    [
      "63565904",
      "68766594898"
    ],
    [
      "64064234",
      "85266004008"
    ],
    [
      "73459785",
      "271819793959"
    ],
    [
      "86379419",
      "479623470403"
    ],
    [
      "212358944",
      "2874928932778"
    ],
    [
      "137627320929",
      "51057120384815048"
    ],
    [
      "-790730465/9",
      "10355958795098/27"
    ],
    [
      "292596031/9",
      "1528884999866/27"
    ],
    [
      "297447031/9",
      "899444101241/27"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,1,7,23,38,43,48,54,77,79: 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 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-28 11:28:49",
  "updated_at": "2026-10-28 11:28:49"
}