{
  "id": 6095,
  "curve_key": "6880931311970863056:-17546414823452615517825658560",
  "ainvs": [
    "0",
    "0",
    "0",
    "-143352735666059647",
    "20308350490107193886372290"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 130.12585704536727,
  "faltings_height": 8.755354325806348,
  "conductor": "837877902601733961103246999529573248471046104",
  "bad_primes": [
    "2",
    "17",
    "23",
    "43",
    "4447",
    "8822239",
    "9340081529363221267876573591"
  ],
  "discriminant": "10368209505862013472789264367074766259536161835862272",
  "regulator": "102081371964861448757.346950941231692484623413216399223990417493970261364",
  "points": [
    [
      "3787234091",
      "231944464397728"
    ],
    [
      "-11994361725034/54289",
      "81188295259488254108/12649337"
    ],
    [
      "-63717868777/169",
      "10010594727765256/2197"
    ],
    [
      "441472627/9",
      "98816186234152/27"
    ],
    [
      "37085072170/121",
      "3024154650391010/1331"
    ],
    [
      "50577646321/324",
      "7680634860145103/5832"
    ],
    [
      "9845643444019/52441",
      "1325579837889527504/12008989"
    ],
    [
      "27821079492921/151321",
      "24057500199652660778/58863869"
    ],
    [
      "65895007605373/863041",
      "2510967927667103806214/801765089"
    ],
    [
      "73867808561066/151321",
      "480575559881387604398/58863869"
    ],
    [
      "77493813526519/447561",
      "246576925306805895064/299418309"
    ],
    [
      "87945272342803/241081",
      "481688524238209745504/118370771"
    ],
    [
      "163009976472017/654481",
      "123780103901550255358/529475129"
    ],
    [
      "200638496008633/274576",
      "2515717415395246704301/143877824"
    ],
    [
      "2071876749637501/12047841",
      "36015112609708608022778/41818056111"
    ],
    [
      "4157825023170998/22118209",
      "6047942239649960436796/104021936927"
    ],
    [
      "33448815372866853/40998409",
      "5546448119454114002708254/262512812827"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,19,23,31,37,51,57,81,93,112: 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 02:21:57",
  "updated_at": "2026-10-29 02:21:57"
}