{
  "id": 93,
  "curve_key": "138640006161934808497729:-59772463447882225317598229177992033",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2888333461706975177036",
    "69181091953326695958744591394960"
  ],
  "rank_lower_bound": 16,
  "naive_height": 160.15170629249525,
  "faltings_height": 11.333679917886252,
  "conductor": "2134765245448937756484936235371093624988033998420670",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "19",
    "37",
    "113",
    "227",
    "7623349",
    "10859470707877171952191399994467277"
  ],
  "discriminant": "-525428654379535377518565414066223922787670130763896329790210867200",
  "regulator": "105196939230354.8297989405772618228792201639412619546898155735467441105",
  "points": [
    [
      "37416111048",
      "3673146956976196"
    ],
    [
      "56645298168",
      "-9344961308712044"
    ],
    [
      "31696413064",
      "-3078242980812300"
    ],
    [
      "38166459504",
      "-3813140617681124"
    ],
    [
      "16981380160",
      "-5003015355085620"
    ],
    [
      "16633886728",
      "5073377832734196"
    ],
    [
      "-4372609640",
      "9040303267636340"
    ],
    [
      "228360089416",
      "-106387135973699596"
    ],
    [
      "4349900728",
      "7529900571118196"
    ],
    [
      "131565942824",
      "44345489428635380"
    ],
    [
      "141669139928",
      "-50033195706517324"
    ],
    [
      "25410503148",
      "3492047785697456"
    ],
    [
      "32894041496",
      "3124735556097140"
    ],
    [
      "-13481531176",
      "10279596157927796"
    ],
    [
      "168559260328",
      "66117003092951796"
    ],
    [
      "24095569528",
      "3684394938234996"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "New curve of rank >= 16, found as the specialization T = 1387/2 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier (Acta Arith. 82 (1997), sextuple {0,55,314,378,1007,1036}), located by a staged Nagao-sum sieve; submitted for its small conductor at this rank. 16 independent points certified by positive-definite Neron-Tate height pairing.",
  "created_at": "2026-06-12 02:09:39",
  "updated_at": "2026-07-01 22:37:40"
}