{
  "id": 6481,
  "curve_key": "42286385396521:-297035826332178468565",
  "ainvs": [
    "1",
    "0",
    "1",
    "-880966362428",
    "343791392248380062"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 94.28076886560339,
  "faltings_height": 5.814687831991175,
  "conductor": "185468216178437434884828822672318",
  "bad_primes": [
    "2",
    "3",
    "30911369363072905814138137112053"
  ],
  "discriminant": "-7301141798080368061676171433318470388",
  "regulator": "8138762136.36682788579547157657060776848139375534081781942791294637",
  "points": [
    [
      "6986796/25",
      "43177970429/125"
    ],
    [
      "16673264",
      "-67984691787"
    ],
    [
      "3083607/49",
      "184254201853/343"
    ],
    [
      "22619694/25",
      "-67068706882/125"
    ],
    [
      "986911953/1681",
      "-11745156790099/68921"
    ],
    [
      "127302963/2809",
      "-82083000483793/148877"
    ],
    [
      "6330866184/6241",
      "346270053981763/493039"
    ],
    [
      "46934405997/29584",
      "8719637976734743/5088448"
    ],
    [
      "2421474",
      "3521424142"
    ],
    [
      "-27804",
      "606861730"
    ],
    [
      "231423",
      "390153115"
    ],
    [
      "331323",
      "296950411"
    ],
    [
      "709809",
      "275499937"
    ],
    [
      "2233824",
      "3084751333"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,15,21,30,41,53,79,86,104,121: 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 14, proved: 14 independent points listed, matching the 2-descent upper bound. Torsion trivial.",
  "created_at": "2026-11-04 02:11:53",
  "updated_at": "2026-11-04 02:11:53"
}