{
  "id": 6019,
  "curve_key": "3824799707694934655029681:-6620790414168133680591671534564736745",
  "ainvs": [
    "1",
    "0",
    "0",
    "-79683327243644471979785",
    "7662951868243514445636723533081241"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 169.81064500128969,
  "faltings_height": 12.131691537939801,
  "conductor": "63305126973580414805462604484667490411184475286",
  "bad_primes": [
    "2",
    "3",
    "7",
    "29",
    "53",
    "103",
    "110984749",
    "6734596097",
    "12738070350496675164301"
  ],
  "discriminant": "7013011673713303510478545054662554139241277905161757843047966480924672",
  "regulator": "272088356553313.466406608776231237990481967144359609898838323888029642056",
  "points": [
    [
      "-316305655622",
      "34944252003491683"
    ],
    [
      "-309586088474",
      "51575079901284463"
    ],
    [
      "-245692617182",
      "111397412400710323"
    ],
    [
      "-211887782342",
      "122612788367841379"
    ],
    [
      "47855524698",
      "62922633539498403"
    ],
    [
      "103004141284",
      "23411440992171721"
    ],
    [
      "208794139066",
      "11310027647476963"
    ],
    [
      "213888224314",
      "20115108151877731"
    ],
    [
      "233279213050",
      "42063574392268771"
    ],
    [
      "247402737850",
      "55606833610919779"
    ],
    [
      "256807699066",
      "64312993087223971"
    ],
    [
      "426943002754",
      "226861028864517235"
    ],
    [
      "560200293466",
      "372597132746865571"
    ],
    [
      "569521819834",
      "383417068799385571"
    ],
    [
      "653478757738",
      "484406068887023443"
    ],
    [
      "5370956227954",
      "12430467095275060411"
    ],
    [
      "35589170296746250/380689",
      "7540856873338706883946427/234885113"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,5,17,24,30,43,47,53,68,73: 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": "2026-10-28 11:28:05",
  "updated_at": "2026-10-28 11:28:05"
}