{
  "id": 6474,
  "curve_key": "4935580839922934032:-11129674384008582520746129344",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-102824600831727792",
    "12881567608358874491069136"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 129.1588248399884,
  "faltings_height": 8.645484462896203,
  "conductor": "10968571582957756733620746557606511621425738596368",
  "bad_primes": [
    "2",
    "3",
    "59960213",
    "1669087579",
    "2283318757093803691254799261933"
  ],
  "discriminant": "-2105965743927889292855183339060450231313741810502656",
  "regulator": "7901616115298367.49752970199723317868942448738408163784753327730500705698",
  "points": [
    [
      "19074794565",
      "2634079217927166"
    ],
    [
      "29848310342",
      "-5156495811192886"
    ],
    [
      "100962104189/25",
      "31982098372021162/125"
    ],
    [
      "260750153901/169",
      "-130479819496897662/2197"
    ],
    [
      "370918916841/784",
      "-183837189041796627/21952"
    ],
    [
      "1409426519000/4489",
      "1022092135403846228/300763"
    ],
    [
      "127210182180/841",
      "21664567053080664/24389"
    ],
    [
      "30532832581/225",
      "-4031741181348154/3375"
    ],
    [
      "-126988635/4",
      "-32113756943157/8"
    ],
    [
      "-369830226",
      "570882674874"
    ],
    [
      "148787080",
      "936153630876"
    ],
    [
      "162890216",
      "674127941348"
    ],
    [
      "173342526",
      "515968844538"
    ],
    [
      "175593814",
      "490225191114"
    ],
    [
      "178759556",
      "461460094792"
    ],
    [
      "630618696",
      "14100455898468"
    ],
    [
      "2172968664",
      "100248465083964"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,2,10,26,56,67,87,90,132,136: 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 02:11:02",
  "updated_at": "2026-11-04 02:11:02"
}