{
  "id": 6072,
  "curve_key": "353455526443056433617:-8006568451288215237512254528281",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-7363656800897009034",
    "9266861635276348502900472777"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 142.3156301020596,
  "faltings_height": 9.858052745979801,
  "conductor": "1020148663534491085865258736935914804554554",
  "bad_primes": [
    "2",
    "7",
    "11",
    "103",
    "109",
    "739",
    "798425838518175588601339206219617"
  ],
  "discriminant": "-11543780925876849096687974021704683194625115019429619900416",
  "regulator": "344738918699780175.9647790608215740166741605965160235153720205141847755",
  "points": [
    [
      "-3200127993",
      "7720005648039"
    ],
    [
      "-1506744623",
      "130159428485239"
    ],
    [
      "388161201",
      "80417836692087"
    ],
    [
      "67691977137",
      "17597955786904023"
    ],
    [
      "7103557195057",
      "18932750391507478903"
    ],
    [
      "-22649953662551/10201",
      "124792732443855745403/1030301"
    ],
    [
      "15293971003/9",
      "1100296546419503/27"
    ],
    [
      "19392927865/9",
      "1575379415016301/27"
    ],
    [
      "178697012481/49",
      "60307856626730609/343"
    ],
    [
      "7367356222297/14161",
      "125842534015437364497/1685159"
    ],
    [
      "8445528752455/2209",
      "19970182429736924169/103823"
    ],
    [
      "51041794437979/4489",
      "355303468820489595013/300763"
    ],
    [
      "78979085317969/3721",
      "696469095889782303747/226981"
    ],
    [
      "112014933222459/121801",
      "2431769960486981752667/42508549"
    ],
    [
      "3483187053358343/822649",
      "173380151438311457573429/746142643"
    ],
    [
      "7035718989135505/2024929",
      "461282819695437823011417/2881473967"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,2,22,36,37,47,82,84,97,105: 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 21:14:37",
  "updated_at": "2026-10-28 21:14:37"
}