{
  "id": 6172,
  "curve_key": "10933524480289020976801:-1071053247587413778269021021068145",
  "ainvs": [
    "1",
    "0",
    "0",
    "-227781760006021270350",
    "1239644962466450800403457742596"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 152.23836198719215,
  "faltings_height": 10.637457019943717,
  "conductor": "921696670794521859371340115713061536866663911815042",
  "bad_primes": [
    "2",
    "3",
    "7",
    "10463",
    "2097405985705915765239278809485264484980325027"
  ],
  "discriminant": "92511493199181681140867470244016054332096813848356245845819392",
  "regulator": "3751194039769578587125.7650982939562058037311580917546064443748586479716523",
  "points": [
    [
      "-15841399770",
      "934153763484774"
    ],
    [
      "5360368764",
      "415536936027810"
    ],
    [
      "6384319084998890",
      "510119440091902353886544"
    ],
    [
      "-221494645289695420524/19141552609",
      "4039001423669049617394234987402/2648291228112977"
    ],
    [
      "-1363912545331659540/133795489",
      "2448130679338399862032971822/1547612421263"
    ],
    [
      "-5369639589865476/326041",
      "134765946799093800888486/186169411"
    ],
    [
      "-3749671525378884/237169",
      "108903600415519921152078/115501303"
    ],
    [
      "-3252252580728060/896809",
      "1206453736716114451852182/849278123"
    ],
    [
      "-340499430852724/1500625",
      "2088935024695739270783426/1838265625"
    ],
    [
      "-17397448923876/2809",
      "231255297531015154362/148877"
    ],
    [
      "50336223699048/3721",
      "180701954652924262698/226981"
    ],
    [
      "1361974277668620/128881",
      "5208975341000668470366/46268279"
    ],
    [
      "5163500908779066/769129",
      "76971896342134066073598/674526133"
    ],
    [
      "5826225655650876/1423249",
      "1040866797210302448655122/1697936057"
    ],
    [
      "16036567836331644/1452025",
      "466530002089710596871162/1749690125"
    ],
    [
      "53047264366535712/2271049",
      "10073435958680582219751222/3422470843"
    ],
    [
      "2020390374582514900/297459009",
      "392712921895892515486045078/5130275528223"
    ],
    [
      "22867048548802998204/221622769",
      "108235145670274904606263308174/3299298162103"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,8,18,22,27,35,49,65,71,103: 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 18, proved: 18 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-10-30 14:39:48",
  "updated_at": "2026-10-30 14:39:48"
}