{
  "id": 3605,
  "curve_key": "1259065830220573719144293521:-45137885440531868532321585864508316672569",
  "ainvs": [
    "1",
    "0",
    "0",
    "-26230538129595285815506115",
    "52242922963576365663861406254548148417"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 187.22108110517578,
  "faltings_height": 13.467792453813214,
  "conductor": "18013703274881884027646086485877363482258088098390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "29",
    "31",
    "43",
    "89",
    "107",
    "881",
    "1019",
    "2557",
    "70003",
    "168554317",
    "186440364443077"
  ],
  "discriminant": "-24015432858013284750880854644069508278550548303172558995669136301962240000000",
  "regulator": "60166503614881545458.2558016767171747379225648736457691244405193977634552",
  "points": [
    [
      "1138246283010394",
      "38401657162377707818273"
    ],
    [
      "-55907139067767097016/23145721",
      "1121909348831440486400689410083/111354063731"
    ],
    [
      "-43664100501439929122/7823209",
      "108919047245841188950637650525/21881515573"
    ],
    [
      "-123613328914271426/22201",
      "16762363226032609673849237/3307949"
    ],
    [
      "188555470717576/49",
      "987388868875899999559/343"
    ],
    [
      "234590353485166/625",
      "101802973065605118303889/15625"
    ],
    [
      "1033155527863279/196",
      "21332681436352375499747/2744"
    ],
    [
      "5707723131764494/1681",
      "105083923308329167742273/68921"
    ],
    [
      "29901188062769134/6241",
      "2980634917253163084189607/493039"
    ],
    [
      "112173600309774766/1352569",
      "11130628389353458171044553691/1573037747"
    ],
    [
      "115314076173532654/57121",
      "37429357790935070076355847/13651919"
    ],
    [
      "13423916599354134162/4765489",
      "8741075532634761300186356187/10403062487"
    ],
    [
      "39002962268941280686/14691889",
      "64635832188531325878843106481/56314010537"
    ],
    [
      "170968571998919373049/41165056",
      "1020941246659273560027570103013/264114999296"
    ],
    [
      "73296498463965346894/107972881",
      "6613714709074224972851579116223/1121946206471"
    ],
    [
      "908402938910805783214/312193561",
      "4107360266103865771529190966917/5516148029309"
    ],
    [
      "26418355633818949787614/3699194041",
      "3405889221909462084478379022777173/224988680767661"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -3/2 of the rank-17 fibration of X1092, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #1958 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:09:14",
  "updated_at": "2026-09-29 19:09:14"
}