{
  "id": 3677,
  "curve_key": "137558881840531871804030233:-1697267212664990108728700790998891447165",
  "ainvs": [
    "1",
    "1",
    "0",
    "-2865810038344413995917296",
    "1964429644286988908697797224491158820"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 180.6596761248368,
  "faltings_height": 12.993208352185937,
  "conductor": "3682590235087728259825836306",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "37",
    "53",
    "71",
    "131",
    "199",
    "311",
    "769",
    "1721",
    "3449"
  ],
  "discriminant": "-160743912861066581276481712926186402389403182140197454927568199353525416596",
  "regulator": "2750799115.9189545545022929235941300794876514352936999277",
  "points": [
    [
      "-383025968802",
      "1733757958572405504"
    ],
    [
      "1037950173966",
      "328766027196977472"
    ],
    [
      "4731702660639/4",
      "3833930584977621531/8"
    ],
    [
      "-695429277029154607/2070721",
      "5064730877937872594995289171/2979767519"
    ],
    [
      "133684452108949/121",
      "509977057101565617698/1331"
    ],
    [
      "14480195553534611/18769",
      "1185804063999412349924429/2571353"
    ],
    [
      "72326176007424611/12769",
      "18671852361674659717383461/1442897"
    ],
    [
      "1476545960608361469/908209",
      "1095643315373821366985227509/865523177"
    ],
    [
      "14180442584727801489/2647129",
      "51021030284237192670183634926/4306878883"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -413/1592 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:31:29",
  "updated_at": "2026-09-29 19:31:29"
}