{
  "id": 6472,
  "curve_key": "9671003216434372761:-30170268465876112421342313405",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-201479233675716099",
    "34919292256244938536223369"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 131.15330892481734,
  "faltings_height": 8.746586258894876,
  "conductor": "217595709279500935445516459956147588999883282238",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "7086647963253736811",
    "7384566114317459889120451"
  ],
  "discriminant": "-3317464183675271261802343948491426141892220521000548",
  "regulator": "1625485584276615.32399401799947593183256931240581403823355457489684751514",
  "points": [
    [
      "2346652699/9",
      "9036213130705/27"
    ],
    [
      "759553880904",
      "-661969612832783717"
    ],
    [
      "245366032501/2601",
      "542926973543005670/132651"
    ],
    [
      "212137491375/676",
      "-28323255010852937/17576"
    ],
    [
      "1576919133968/6889",
      "-509496980082911585/571787"
    ],
    [
      "158928767164/2025",
      "-403327781762544053/91125"
    ],
    [
      "1603468271744/3025",
      "1460445789617400437/166375"
    ],
    [
      "2249723641813/3249",
      "2792656779854299249/185193"
    ],
    [
      "201911530174/225",
      "81053164117841713/3375"
    ],
    [
      "-518317363",
      "319665286145"
    ],
    [
      "-422281746",
      "6685884092743"
    ],
    [
      "142182510",
      "3024298541447"
    ],
    [
      "270208878",
      "454322261767"
    ],
    [
      "1134172247/4",
      "6129031303495/8"
    ],
    [
      "357628001",
      "2933165098754"
    ],
    [
      "1601383550",
      "61796518139363"
    ],
    [
      "3803084368/9",
      "135627045145121/27"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,6,51,52,83,90,110,114,120,140: 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 02:10:47",
  "updated_at": "2026-11-04 02:10:47"
}