{
  "id": 3616,
  "curve_key": "2166777529270000941366417844585628425:-1781756596116064673125821524326201406735443535773073125",
  "ainvs": [
    "1",
    "0",
    "1",
    "-45141198526458352945133705095533926",
    "2062218282541741516059786146320833327182658297331748"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "naive_height": 250.99891320619653,
  "faltings_height": 18.962420951069028,
  "conductor": "1276790687761151076804421275353458888576233831160016970956831646271429350",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "31",
    "37",
    "41",
    "43",
    "53",
    "107",
    "109",
    "2777",
    "371682981688163",
    "1160163369385000545668134854830921"
  ],
  "discriminant": "4049884909363351079009747519467402173327926713990480440831144208879352817953741157862530932627482073062500",
  "regulator": "1302173947120592844163397163362.3637063438983675814410249910663982650829258653975",
  "points": [
    [
      "-10616214366335638465753004756106957/58056219649707889",
      "906805792640893168929398558413357022370332620370497/13988563858933872218471287"
    ],
    [
      "-47401850193040061684735668461391/911586271245169",
      "1798274627860929242341698392094860037131546148513/27523056643948238845303"
    ],
    [
      "-6860629016046081788435826033/96596018401",
      "2103690396379225937151053525694944721902909/30021945923012399"
    ],
    [
      "-17789168336836090738908727947/256955720464",
      "9076257229721264409604324913622836839562707/130252910348965312"
    ],
    [
      "-41061721384451549602756974/335073025",
      "465248365516035982901596766466019078061/6133511722625"
    ],
    [
      "-33146368578388447326768/143641",
      "752714905442465815286748543242929/54439939"
    ],
    [
      "140238058970121037429897194/5686215649",
      "13312309115450245093388225413264537105931/428780463444143"
    ],
    [
      "363166183074488964798358067/166384201",
      "6888652215342413815834703370178631465109/2146189808699"
    ],
    [
      "742389017711185723529771052/1621431289",
      "18161689432312489049308987176368122266421/65290173714163"
    ],
    [
      "42421222474004843018893457417/179321759296",
      "5162695932982202376358863527068439077086009/75936309478521344"
    ],
    [
      "12137434957966143654748586706/51388809481",
      "788047466012043995332170679363725955018976/11649380610057371"
    ],
    [
      "17378357962853082980757131254/3200956929",
      "2289196619657494124519483718976122900052936/181100540172033"
    ],
    [
      "17727580210753660101691959168/422893991809",
      "4292060718369669519353091636478471998829397/275009231555368127"
    ],
    [
      "195237226174777415604941608653/5233607893264",
      "248323356586200900581205256111606838100859807/11972966646283198912"
    ],
    [
      "6589282642946879596055592917208/14905182082729",
      "15061346667831792412872597021720754111703921537/57544779285979753067"
    ],
    [
      "373652459774951885300610168509243/1058961132472489",
      "5975121453110258851495017627063288131378027253447/34460377482240743258987"
    ],
    [
      "469992367080322064122327860161913/1978612115817649",
      "6060802988505069201556481201754593560117606444067/88011818840669525034857"
    ],
    [
      "1624001918606182552653283429609818/2955639883445209",
      "60794270709564229248687887453746005256674420357553/160685717908485893116573"
    ],
    [
      "3213133030828216408780295039245092/16220278456346449",
      "61747610322577858415261076708552232257542808235372/2065796124422008140648793"
    ],
    [
      "45573406533310852044341923169065218/3262266128295001",
      "9727856815112443848442936942876037178461907793956967/186328411012495479161251"
    ],
    [
      "166260132949648858647422792394664167/723585178872886201",
      "38047069563414181352062784243645578749739028090672441/615509122468177238407744301"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -293/64 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (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 19:20:11",
  "updated_at": "2026-09-29 19:20:11"
}