{
  "id": 216,
  "curve_key": "14023872430665521304793969:-52511984964278614476420631331018287753",
  "ainvs": [
    "1",
    "0",
    "0",
    "-292164008972198360516541",
    "60777760375298123458072491954931825"
  ],
  "rank_lower_bound": 17,
  "naive_height": 173.70840984880002,
  "faltings_height": 12.17138533248092,
  "conductor": "8229621766982592642433268362527136439092061141374442470",
  "bad_primes": [
    "2",
    "5",
    "11",
    "29",
    "37",
    "41",
    "61",
    "257",
    "2467",
    "4177",
    "40298971",
    "453713587",
    "575746473701180535499"
  ],
  "discriminant": "319660562013917792358156721464086339946753006672777251625449427814400",
  "regulator": "605706094414059953.433928438056900702744283818617694394403423434391605716",
  "points": [
    [
      "-38718845802698642844526436/105831648077401",
      "-375098011016010771236367933056744517569/1088737893845506994851"
    ],
    [
      "370022648858",
      "57729896660684391"
    ],
    [
      "813867360018",
      "-601735013298569809"
    ],
    [
      "51388025011062/169",
      "-16041282810910889293/2197"
    ],
    [
      "1742212142545418/5041",
      "11787551290092658020681/357911"
    ],
    [
      "138421495063902/49",
      "-1600711642945571193647/343"
    ],
    [
      "1523744473018",
      "1775786428781568391"
    ],
    [
      "88651233252202/289",
      "-22108110499592240017/4913"
    ],
    [
      "72435267588973433/18496",
      "-19318466609689318953185999/2515456"
    ],
    [
      "308271320498",
      "2714843230760431"
    ],
    [
      "82306269319150/729",
      "3365202373896362951845/19683"
    ],
    [
      "2782325464450/9",
      "37096591825050565/27"
    ],
    [
      "5790971164122842/18769",
      "6054012515438553117423/2571353"
    ],
    [
      "-5029167919947/16",
      "-22313592130959039811/64"
    ],
    [
      "1262165031167/4",
      "18298327651158693/8"
    ],
    [
      "556113986993050/1849",
      "841917866240162077525/79507"
    ],
    [
      "2466561849275650/289",
      "122260608489486622716095/4913"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Specialization at T = -2407/2 of the Mestre/Fermigier family y^2 = r(x,T), where r is the degree-<=4 remainder in p6(x-T)*p6(x+T) = g(x)^2 - r (g monic of degree 6), p6(x) = prod_i(x-a_i) on the sextuple (a) = (-44, -60, -6, 110, 94, -94). Located by a Mestre-Nagao sieve of this family for small-conductor high-rank specializations. Seventeen independent rational points were found by rational-x enumeration on the quartic plus a direct minimal-model x = n/q^2 sieve; rank >= 17 follows from the positive-definiteness of their 17x17 Neron-Tate height-pairing matrix, computed independently in Sage and Magma. Conductor by Tate's algorithm. Proven lower bound on the Mordell-Weil rank (no exact-rank, Selmer, or BSD claim).",
  "created_at": "2026-06-25 21:52:44",
  "updated_at": "2026-07-01 22:35:41"
}