{
  "id": 160,
  "curve_key": "3514491230321299879293372441:-211680502645018272939774419486596394068989",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-73218567298360414151945259",
    "245000581765085750173970908953765294265"
  ],
  "rank_lower_bound": 19,
  "naive_height": 190.3117934033658,
  "faltings_height": 13.744300895897728,
  "conductor": "3193612294999847993147255601045320568117070630221566159701261290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "23",
    "29",
    "31",
    "43",
    "16657",
    "29873",
    "2175553654838803",
    "149259273131621162380144645571"
  ],
  "discriminant": "-809533846760755463057458884959863139807213987649788585257426576417408765702500",
  "regulator": "423708814536549837.7305076307123902558268187152316566188047402169947718710324",
  "points": [
    [
      "5549704953011",
      "3096083152855087682"
    ],
    [
      "13056506698121",
      "38920366941834097517"
    ],
    [
      "212900947646",
      "-15146680585140585313"
    ],
    [
      "11070733798556",
      "28129323372160311527"
    ],
    [
      "-4794571897764",
      "-22041663447857995993"
    ],
    [
      "4218305221016",
      "-3347128863109670413"
    ],
    [
      "5564955439436",
      "-3143585857583770243"
    ],
    [
      "22114485495959/4",
      "-24250416298451057129/8"
    ],
    [
      "5281352058011",
      "2370358361443582307"
    ],
    [
      "6596721361454",
      "-7004705656918603993"
    ],
    [
      "9217322631611",
      "-18794053512472866493"
    ],
    [
      "5394735087236",
      "2647577719102945757"
    ],
    [
      "5211535300685",
      "-2228287716765803110"
    ],
    [
      "1852282363436",
      "10757982573182078807"
    ],
    [
      "5751888420311",
      "-3761956701013851193"
    ],
    [
      "5242366838660",
      "2287980724263201245"
    ],
    [
      "-7214909794804",
      "19942279400410835837"
    ],
    [
      "5258984909246",
      "-2322195160345708513"
    ],
    [
      "8465892054285",
      "-15228327292608313255"
    ]
  ],
  "submitter": "cocoxhuang",
  "commentary": "New curve of rank ≥ 19 and and log conductor 146.224, found as the specialization t = 10806/5 of the 2-parameter Mestre rank-12 family over Q(t) used by Fermigier in 'Une courbe elliptique définie sur Q de rang ≥ 22' (Acta Arith. 82 (1997)) — here at family parameters (u,v) = (4,6), sextuple {−1146, −2304, −654, 3054, 2880, −1830} — located by a discriminant-gated exhaustive specialization scan crossed with a stagedNagao-sum sieve; 19 independent points certified by positive-definite Néron–Tate height pairing. Conductor N (log N ≈ 146.22) is squarefree apart from 3², with bad primes 2, 3², 5, 13, 19, 23, 29, 31, 43, 16657, 29873, 2175553654838803,149259273131621162380144645571.",
  "created_at": "2026-06-25 02:48:52",
  "updated_at": "2026-07-01 22:30:42"
}