{
  "id": 6100,
  "curve_key": "18077337552204685838161:-2490522562821252934467777646182745",
  "ainvs": [
    "1",
    "0",
    "0",
    "-376611199004264288295",
    "2882549262493214037198461362761"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 153.79560124369695,
  "faltings_height": 10.720642504450701,
  "conductor": "13406169159886136449996482619880669444469797358",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "41",
    "7519095045599",
    "4954042034786895640115339629"
  ],
  "discriminant": "-170837438297692389492480085766629110687115306414695147713691648",
  "regulator": "25934491367920437015.9624329966909241210536010521313989485511187287986418",
  "points": [
    [
      "-161769047916884870/7733961",
      "27280569055819966351230689/21508145541"
    ],
    [
      "-16464155971914/1849",
      "186969055729203574575/79507"
    ],
    [
      "293092238054/25",
      "35052303443953873/125"
    ],
    [
      "654260371926/25",
      "413639767639764561/125"
    ],
    [
      "3346027178820/289",
      "1338034692867415527/4913"
    ],
    [
      "5676884921400/529",
      "3372740150568346173/12167"
    ],
    [
      "47627829240189/8464",
      "755564552019828862509/778688"
    ],
    [
      "490355510821638/52441",
      "5074573926802837433361/12008989"
    ],
    [
      "563321157155526/25",
      "13370076350502270590961/125"
    ],
    [
      "1707629754913566/73441",
      "51502921563012291376323/19902511"
    ],
    [
      "2546876064655230/237169",
      "31970378849756552198763/115501303"
    ],
    [
      "3586828053645606/198025",
      "124730953411489172939961/88121125"
    ],
    [
      "35219673324408804/1907161",
      "3929106860208310484289201/2633789341"
    ],
    [
      "161786850503052390/51529",
      "65073839623394425783758183/11697083"
    ],
    [
      "1014912032549652006/28249225",
      "897418342299498335885250759/150144630875"
    ],
    [
      "2178066246574532622/227919409",
      "1360111483337484040958400837/3440899317673"
    ],
    [
      "49612367760298764190/3142835721",
      "164446731506288325688754744969/176190513354981"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,8,14,30,54,72,101,108,109,130: 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": "2026-10-29 02:28:47",
  "updated_at": "2026-10-29 02:28:47"
}