{
  "id": 3604,
  "curve_key": "3282135420667166248908801:-5949718618294298367125436934830003201",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-68377821263899296852267",
    "6886248400820680528377823128414459"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 169.35281455036392,
  "faltings_height": 11.867968110127704,
  "conductor": "3199991341836188371521276362329878718158175687790",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "31",
    "43",
    "101",
    "35627957",
    "693914587",
    "1248560577878553982360441"
  ],
  "discriminant": "-24672238085935922757468883416984274683524930274694737461594086400000",
  "regulator": "1218534680544749405.81763555708802496069346323552753443268406699297125097",
  "points": [
    [
      "-279263125773",
      "64826905805120106"
    ],
    [
      "-270110166413",
      "75157901485298466"
    ],
    [
      "-205241909343",
      "110790820956250166"
    ],
    [
      "104569831777",
      "29655411452365416"
    ],
    [
      "152682716267",
      "2340480902026666"
    ],
    [
      "274740645317",
      "94011410025204116"
    ],
    [
      "1212475988827",
      "1306306530940282666"
    ],
    [
      "-735089341029/25",
      "11773501776616385466/125"
    ],
    [
      "1336395299011/9",
      "71059651910996654/27"
    ],
    [
      "43264571198663/289",
      "10846120617756202558/4913"
    ],
    [
      "85092069225883/529",
      "85467786526525901222/12167"
    ],
    [
      "350999001245423/2209",
      "597087334954296260518/103823"
    ],
    [
      "3034304533368923/18769",
      "19440780269873393046298/2571353"
    ],
    [
      "13003600863099243/16129",
      "1412943017784926213339478/2048383"
    ],
    [
      "62787757944290083/413449",
      "564456622045895783729262/265847707"
    ],
    [
      "117064484034825963/66049",
      "39639951077770273877417578/16974593"
    ],
    [
      "134490217056362047/1371241",
      "53816381861039536883156926/1605723211"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -2 of a rank-17 elliptic K3 family (member P = 2G + theta of C546 in https://gist.github.com/7fff-zip/58764130a98380def8d555e30ba81344, in reduced coordinates y^2 = x^3 - 27*c4(t)*x - 54*c6(t), c4 = 229266544691230630042225 + 1148767151849671983980280*t + 1683055912133375613928320*t^2 + 437075683846550943081920*t^3 - 419700913360243030971880*t^4 - 413476672102570136085360*t^5 + 296474488499927445158320*t^6 + 353395116108885163700480*t^7 + 85386537915381926875456*t^8, c6 = -110117600739533363968141608029430025 - 832583143909661430864544305147730260*t - 2258777613778127645018144727033322776*t^2 - 2323066840605949954916562239379172800*t^3 + 4224411691620789521802920064397980*t^4 + 760246669056877381267793145815769720*t^5 - 982276963083748004851457103694787400*t^6 - 597764504390070426967497552771547104*t^7 + 374646738137646635315808548695924200*t^8 + 71041369628477641221666859558448960*t^9 - 272311587156276263196050039283673920*t^10 - 153971474450137833790103496028596480*t^11 - 25015849076229626982910761017951104*t^12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:09:04",
  "updated_at": "2026-09-29 19:09:04"
}