{
  "id": 6013,
  "curve_key": "881808454575244521:-774499246154708361649806069",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-18371009470317594",
    "896411169123664823192600"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 123.96225376694669,
  "faltings_height": 8.28229883544149,
  "conductor": "154515334763674237217989679743634659112490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "127",
    "11953",
    "1555607",
    "727023666511836896234165233"
  ],
  "discriminant": "49671851522309902445670619860086554321568269687500",
  "regulator": "1075711595306826.128648202483924995665820436723699349237414859936751204",
  "points": [
    [
      "-140760854",
      "832745793172"
    ],
    [
      "-30105500",
      "1192572699640"
    ],
    [
      "-5237339",
      "996236885662"
    ],
    [
      "54539311",
      "238086434752"
    ],
    [
      "61307566",
      "23654579842"
    ],
    [
      "95226091",
      "102532777417"
    ],
    [
      "97281541",
      "172850744317"
    ],
    [
      "132888196",
      "895383013972"
    ],
    [
      "147594691",
      "1183217753092"
    ],
    [
      "156051826",
      "1352616524722"
    ],
    [
      "277845121",
      "4152110920357"
    ],
    [
      "572397316",
      "13338394383592"
    ],
    [
      "956537566",
      "29300057519842"
    ],
    [
      "5501487139/4",
      "406135211351861/8"
    ],
    [
      "2793135753619/9409",
      "4241910647525474041/912673"
    ],
    [
      "3014875123381/32041",
      "170832869319935138/5735339"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,3,12,26,27,35,38,40,52,55: 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 the sum of -a_p log(p)/p over 5 <= p <= 199; the sets scoring at least 28 were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.\r\n",
  "created_at": "2026-10-28 04:53:45",
  "updated_at": "2026-10-28 04:53:45"
}