{
  "id": 6101,
  "curve_key": "2698484030004818223441:-139045685047065799529492078534745",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-56218417291767046322",
    "160932505855565946370965000625"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 148.04093129349943,
  "faltings_height": 10.192719631344191,
  "conductor": "15042348617841095595823355422402529435108652138",
  "bad_primes": [
    "2",
    "3",
    "11",
    "313",
    "6271",
    "55441",
    "2174741",
    "321018989709898828986366637"
  ],
  "discriminant": "182964014843935538155341625068220986965911853390976374341632",
  "regulator": "134341422699397113058.554611561303551637181914443484032584412709827115853",
  "points": [
    [
      "5705390131777",
      "13627856573091991727"
    ],
    [
      "-35371040878452006726575/6877668845961",
      "10107663185076602949879305630608525/18036899756266947291"
    ],
    [
      "-85721404382735639/17131321",
      "39919571680846701156712189/70906537619"
    ],
    [
      "-229586981591383/26569",
      "167326587586137487349/4330747"
    ],
    [
      "-112610142801623/17161",
      "1117922488570261792405/2248091"
    ],
    [
      "362534814121/25",
      "193454135751570691/125"
    ],
    [
      "167422029177521/9025",
      "2011094408790617724721/857375"
    ],
    [
      "181311911513801/10201",
      "2251787401739011648451/1030301"
    ],
    [
      "300555135386593/96721",
      "3833623671194386077337/30080231"
    ],
    [
      "3209475894030121/687241",
      "8840756552466835108523/569722789"
    ],
    [
      "8087708820862921/133225",
      "722034464226775585310299/48627125"
    ],
    [
      "21493884922758529/1408969",
      "2825093389446061808336293/1672446203"
    ],
    [
      "22716088720035295/6355441",
      "1204866906252662922781385/16022066761"
    ],
    [
      "103048409116308193/21986721",
      "2059554222045356891560991/103095734769"
    ],
    [
      "112918152978254401/28185481",
      "420831374552072597636923/149636718629"
    ],
    [
      "264407833393479881/53333809",
      "24850692167941189521936545/389496807127"
    ],
    [
      "271773475686033745/26697889",
      "110659178805647723442150977/137947992463"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,3,30,44,85,98,101,106,118,127: 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 02:28:56",
  "updated_at": "2026-10-29 02:28:56"
}