{
  "id": 3612,
  "curve_key": "5801886097653644816258693200:-433980362154876805619216980093476792280000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-120872627034450933672056108",
    "502292085827363419331748909982151898288"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 191.783941694339,
  "faltings_height": 13.87327889654447,
  "conductor": "377744506397500932049149835304360449085422198510087093787400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "31",
    "59",
    "495950017",
    "47477125039",
    "11167892699404202375307704232253"
  ],
  "discriminant": "4029775546283096723137009505338922627499213359242882233035478042425962356000000",
  "regulator": "136370476561946243122803.6908268312234518613933011794846798383062542641242533",
  "points": [
    [
      "4843116072103",
      "5521861620285006150"
    ],
    [
      "8741315676994258",
      "817268693594497006196250"
    ],
    [
      "-11407698690033954662/900601",
      "860901498296491425455003850/854670349"
    ],
    [
      "-211883264194251761/19321",
      "60588614747677471488459594/2685619"
    ],
    [
      "23207943709469908/6241",
      "5033680315701532018547100/493039"
    ],
    [
      "49560427024689982/5329",
      "5256087038107639203704850/389017"
    ],
    [
      "140554790083657693/24964",
      "1871073275683010996413971/3944312"
    ],
    [
      "473343312296232148/434281",
      "5518684383817872362650100700/286191179"
    ],
    [
      "1075321192733060722/12769",
      "1106012703616323520277233050/1442897"
    ],
    [
      "1363210227868129918/192721",
      "93358125995544907788964050/84604519"
    ],
    [
      "18454970299364249737/2534464",
      "11574530287760793923853977925/4034866688"
    ],
    [
      "18706546222818044116/2569609",
      "11769798461112706835366154972/4119083227"
    ],
    [
      "27067521920469491682/5442889",
      "62438943659282049937814894850/12698260037"
    ],
    [
      "31527790992358952008/2563201",
      "121491261846973016935799316300/4103684801"
    ],
    [
      "32174774174414738452/6265009",
      "64628403178558830522115436100/15681317527"
    ],
    [
      "194074867633505639911/172225",
      "2703543447949752794907258965766/71473375"
    ],
    [
      "253345157154430352212/35081929",
      "509535684701799146585627984100/207790265467"
    ],
    [
      "5321615386491914066932/679279969",
      "106479912862910242002386573282700/17704073832047"
    ],
    [
      "8995983635450338643502/1668967609",
      "185155286813754542478557138393850/68182333730477"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 5/2 of a rank-17 elliptic K3 family (member P = -3G + 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 = 113915556676586218390225 + 117014247072745494659640*t - 714542170231101375740040*t^2 + 59737931954947719760560*t^3 + 1321595301880580949151920*t^4 - 1928468740555818605289600*t^5 + 1536514504542469295299200*t^6 - 464451616236152639846880*t^7 + 46428990309509190682896*t^8, c6 = -38059341830230470571898103643651225 - 60802697439351169215335193049612020*t + 306907782422718633140882412470699604*t^2 + 350452937805251724377651403468219240*t^3 - 963553613419713777812910016932916800*t^4 - 1073907848531523127380729597230188320*t^5 + 2003891611171001180234808501351087840*t^6 + 1925073232043332626346743369726726096*t^7 - 4737928635455002698341677174065585720*t^8 + 3095917488055497753721277439726477600*t^9 - 978774537199645066029066153236296800*t^10 + 155737640585348222809204520763612480*t^11 - 9967046802486275083949405161786944*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 19:19:13",
  "updated_at": "2026-09-29 19:19:13"
}