{
  "id": 6449,
  "curve_key": "22187002401637203207441:-2845145821024554888112018111912185",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-462229216700775066822",
    "3292992848523606943193733248085"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 154.36138077867193,
  "faltings_height": 10.85387644350041,
  "conductor": "831896611260754035997450667257493457847065982",
  "bad_primes": [
    "2",
    "11",
    "17",
    "19",
    "23",
    "43",
    "443063",
    "683290872278032605040564338731"
  ],
  "discriminant": "1635988019109418827711762446319038294652539423454037724393439232",
  "regulator": "41586334606869.4633418060307616199720175399776032242227561167120888372857",
  "points": [
    [
      "118977449001",
      "-40404258369912709"
    ],
    [
      "690930774761913",
      "-18161504121493260105333"
    ],
    [
      "-43322301054071/2025",
      "-167779641255275087857/91125"
    ],
    [
      "-3854400103703/9409",
      "1703126373223139424987/912673"
    ],
    [
      "26919878350513/3249",
      "33109652196883593355/185193"
    ],
    [
      "210295576129/25",
      "444897157891407/125"
    ],
    [
      "67742426212289/4225",
      "16674580881594796883/274625"
    ],
    [
      "2619433819117/81",
      "3432069573793511275/729"
    ],
    [
      "1059927306588977/24649",
      "30698762449535221500967/3869893"
    ],
    [
      "84595053396952113/2111209",
      "-21496339141827318127653225/3067586677"
    ],
    [
      "268483609309/9",
      "-108174511270133843/27"
    ],
    [
      "33047483789",
      "-4910193013851005"
    ],
    [
      "44063306005",
      "-8275156832229581"
    ],
    [
      "53985770319865/1681",
      "-320107550068739115741/68921"
    ],
    [
      "-20282379035",
      "-2079518504660345"
    ],
    [
      "-604252836101/49",
      "-915092896253694537/343"
    ],
    [
      "2311573806707113/47089",
      "-101618278280495585909469/10218313"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,1,90,97,114,115,130,144,157,172: 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); for the sets with S >= 31, or S >= 30 and one bad prime in that range, or S >= 29 and two or more bad primes, rational points were found by a point search on the quartic y^2 = r(x), and the curves were screened by conductor and by a GRH explicit-formula upper bound on the rank. Rank 17, proved: the 17 listed points come from the point search and are independent, and the 2-descent upper bound (ellrank) is 17. Torsion trivial.",
  "created_at": "2026-11-03 14:23:55",
  "updated_at": "2026-11-03 14:23:55"
}