{
  "id": 6471,
  "curve_key": "151132047308460777:-68854032108124346101168629",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3148584318926266",
    "79692167578956665496808"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 118.98806203795783,
  "faltings_height": 7.906933505800991,
  "conductor": "33903787996443780643530576960241856965080273638",
  "bad_primes": [
    "2",
    "11",
    "1052417",
    "1117661",
    "1425707",
    "1576112047",
    "583055935496865673"
  ],
  "discriminant": "-745883335921763174157672693125320853231766020036",
  "regulator": "7560747297988517.45686189645791250361483723548797643503587117392090421704",
  "points": [
    [
      "7712759406",
      "677330679675496"
    ],
    [
      "4458851068",
      "-297716911599712"
    ],
    [
      "409030611",
      "8198887918628"
    ],
    [
      "2009025414/25",
      "-73493071236398/125"
    ],
    [
      "65097971884/1225",
      "-10714973746977368/42875"
    ],
    [
      "3308891179/100",
      "108321796456313/1000"
    ],
    [
      "-49397828052/3481",
      "71594561107571336/205379"
    ],
    [
      "-1264825589/36",
      "-82796408770637/216"
    ],
    [
      "-17078320806/289",
      "-1197140683733606/4913"
    ],
    [
      "-65076671",
      "94867123637"
    ],
    [
      "-64455556",
      "121909644384"
    ],
    [
      "21266588",
      "149490918448"
    ],
    [
      "47742299",
      "195403426009"
    ],
    [
      "359523527/4",
      "5784054749759/8"
    ],
    [
      "384844871/4",
      "6534942588947/8"
    ],
    [
      "126554177",
      "1306884410890"
    ],
    [
      "-1013701711/25",
      "46889072863578/125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,1,12,30,35,40,59,72,102,105: 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 17, proved: 17 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-11-04 02:10:40",
  "updated_at": "2026-11-04 02:10:40"
}