{
  "id": 756,
  "curve_key": "1875257757834723482353326283441:-2570617409412003664088451304387301918662598761",
  "ainvs": [
    "1",
    "0",
    "0",
    "-39067869954890072549027630905",
    "2975251631263889874076174250349627764668025"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 209.1209505838243,
  "faltings_height": 15.201108329498812,
  "conductor": "449517592123923690953740840316064540448927891518452310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "67",
    "163",
    "509",
    "165391",
    "3490675691035125664582435380215321467"
  ],
  "discriminant": "-7846109474485694297022178534337692317123714544255992769068455706697871501726131200000",
  "regulator": "287537628159239.414303832188130083426853941555116670674844370787940061179",
  "points": [
    [
      "-227701393782940",
      "-255372841238799728605"
    ],
    [
      "-224750577347758",
      "-634816433824237959133"
    ],
    [
      "-190352168431390",
      "-1874751839212055933605"
    ],
    [
      "-167209073188864",
      "-2198357604020881469173"
    ],
    [
      "-142251922744078",
      "-2377851246160330981789"
    ],
    [
      "-85333080776230",
      "-2384881606532678055565"
    ],
    [
      "-82613165318530",
      "-2374645730195290533205"
    ],
    [
      "-37954721663614",
      "-2098424550437393821573"
    ],
    [
      "-21015835294300",
      "-1946025062721869709895"
    ],
    [
      "19980177992810",
      "-1484131026081166508605"
    ],
    [
      "107228482905530",
      "-137734136394032970925"
    ],
    [
      "1145100247631299820/14641",
      "-1117782993191505300403778965/1771561"
    ],
    [
      "1278667755839110",
      "-45206537696318836953605"
    ],
    [
      "-77849147231319305590/477481",
      "-738569541494529421412706257455/329939371"
    ],
    [
      "12469868890099145/64",
      "-850603437354504745447025/512"
    ],
    [
      "203493177758027528/2809",
      "-107895407849306180905506593/148877"
    ],
    [
      "217462539869120",
      "-2182486626266532666955"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization at T = -469/509 of the rank-11 fibration of X163 described by wgxli for ICARM #718. Independently recovered polynomial sections and rational-point search yield 17 points with an exact independence certificate, proving rank >= 17.",
  "created_at": "2026-09-18 01:24:38",
  "updated_at": "2026-09-18 01:24:38"
}