{
  "id": 6016,
  "curve_key": "18500609096023012989121:-2289040448169876340042573344226081",
  "ainvs": [
    "1",
    "0",
    "0",
    "-385429356167146103940",
    "2649352370534867391664975491600"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 153.8162718255798,
  "faltings_height": 10.786762480063917,
  "conductor": "3837683991186327423730835916140464696192710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "1277",
    "3396397",
    "157723717012615131334295214319"
  ],
  "discriminant": "632259396165794733966036546654731253284046569058289651200000000",
  "regulator": "11961016627424.07072823478061145163627136689939930850283041102653517275",
  "points": [
    [
      "-22236254520",
      "474478203307260"
    ],
    [
      "-18362212920",
      "1880297747121660"
    ],
    [
      "-6094769820",
      "2184507092425260"
    ],
    [
      "-297547800",
      "1662531256517340"
    ],
    [
      "4018545480",
      "1079526262747260"
    ],
    [
      "6077191080",
      "729016079251260"
    ],
    [
      "6558111696",
      "635386606363452"
    ],
    [
      "7483590030",
      "429028839218010"
    ],
    [
      "8425649280",
      "3130823531460"
    ],
    [
      "16016046600",
      "764605615862460"
    ],
    [
      "19170661800",
      "1518512191399740"
    ],
    [
      "20679908880",
      "1876862040403260"
    ],
    [
      "43714845480",
      "8326976420047260"
    ],
    [
      "50476885320",
      "10573760283086460"
    ],
    [
      "54625537542",
      "12024734803122072"
    ],
    [
      "1422769755720/169",
      "76091227367613420/2197"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Mestre ten-root construction, roots 0,2,6,13,23,30,39,56,59,70: 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 (with early abort on low partial sums); the sets scoring at least 31 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.",
  "created_at": "2026-10-28 06:03:39",
  "updated_at": "2026-10-28 06:03:39"
}