{
  "id": 220,
  "curve_key": "664432953815666778691825:-549132701009999108371297164497895625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-13842353204493057889413",
    "635570255797456549699738037418817"
  ],
  "rank_lower_bound": 15,
  "naive_height": 164.58729639029724,
  "faltings_height": 11.594497704331756,
  "conductor": "12223008395520638435655400939715776894443327750088254536450",
  "bad_primes": [
    "2",
    "5",
    "19",
    "2887",
    "20611660717",
    "216219438825740695335021821292755331032329"
  ],
  "discriminant": "-4756217026864990828082229613662203105165787694114341605223424000000",
  "regulator": "2299012980980795.1736773300246733262723740839069277093718024770082457",
  "points": [
    [
      "2514318013738/9",
      "3679561913702325293/27"
    ],
    [
      "35031218931168258/170569",
      "5660014854257299777589923/70444997"
    ],
    [
      "2920373190306/25",
      "3093840971560740139/125"
    ],
    [
      "268737294840178/3249",
      "1392139062719172942527/185193"
    ],
    [
      "77950760643761618/1129969",
      "3593459039902576022864833/1201157047"
    ],
    [
      "1079868038566/25",
      "1359257684239148771/125"
    ],
    [
      "5495981224266002/229441",
      "1959028068119665673087321/109902239"
    ],
    [
      "-2334203386631278/44521",
      "327738821395223206667629/9393931"
    ],
    [
      "-105872842798",
      "30238515461284999"
    ],
    [
      "323582351918322",
      "-5820726913620344706361"
    ],
    [
      "16001135916564622/961",
      "2024022591810443849120209/29791"
    ],
    [
      "1116391929791206802/78961",
      "1179532702855065438160211519/22188041"
    ],
    [
      "-70392120718",
      "35512938899164359"
    ],
    [
      "277081493813293058/316969",
      "144594497776810957638668973/178453547"
    ],
    [
      "2513014308877942346562/6869641",
      "-125977339136208237332006595248701/18005329061"
    ]
  ],
  "submitter": "Edgar Costa",
  "commentary": "Specialization at T = -281 of the Mestre/Fermigier family y^2 = r(x,T) on the sextuple (a) = (1608, -870, -1080, -642, 1542, -558) [r = degree-<=4 remainder in p6(x-T)p6(x+T) = g^2-r, g monic degree 6, p6(x)=prod(x-a_i)]. Located by a Mestre-Nagao sieve of this family. Fifteen independent rational points were obtained from the low-height Mestre quartic cover; rank >= 15 follows from the positive-definiteness of their 15x15 Neron-Tate height-pairing matrix, verified independently in Sage and Magma. Conductor by Tate's algorithm. Proven lower bound on the rank (no exact-rank/Selmer/BSD claim).",
  "created_at": "2026-06-25 22:06:54",
  "updated_at": "2026-07-01 22:42:38"
}