{
  "id": 3762,
  "curve_key": "932981621952857847571014086478489792058925361:-28349467195011476773080820539643818353179832874412494979279452488745",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-19437117124017871824396126801635204001227612",
    "32811883327559579598478031200165053487840164858566722434425599135"
  ],
  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 310.6408782258106,
  "faltings_height": 23.724213425169868,
  "conductor": "3174268000626664447890199710966144968041105363299985047543903707586610176360119017465386409590737398259154",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "19",
    "29",
    "31",
    "37",
    "59",
    "61",
    "264269",
    "31343423",
    "1992787623241301574051210793060335615034084525434701774079172167997164741244609"
  ],
  "discriminant": "4876130810587559530809237100161753709458594464826856621387065289527239402714075379609078894389508552780965877331034581333695639552",
  "regulator": "414712471196139643006893396360.0060472924234499548491848395514918211640525720938933070341246909",
  "points": [
    [
      "-17750395349344523060833/4",
      "-1423900166717069213900657335158889/8"
    ],
    [
      "2995893456954080622401605/961",
      "1493954349496369391889909009388892075/29791"
    ],
    [
      "4083055657741700772823",
      "146693816163456384642462165431717"
    ],
    [
      "6012914438374262316885007/2209",
      "-881837700050419790679101116976187659/103823"
    ],
    [
      "27340242870829431132853",
      "4465190243340253720220786493880037"
    ],
    [
      "1875906925751383848145",
      "-54323359920007408885045449375091"
    ],
    [
      "1646427200981291561173",
      "-72616060831366097055243628953883"
    ],
    [
      "20789565851368042701971",
      "2934978493806489127554218582102221"
    ],
    [
      "2186301623141453330623",
      "27691480063937562458311779814667"
    ],
    [
      "2593684991417824238379203/961",
      "103656052603639970139335113974855347/29791"
    ],
    [
      "-34204796983901709808571/49",
      "73597241321285289606469713587253203/343"
    ],
    [
      "1748643535490112880981",
      "-64577211615188397584911296260923"
    ],
    [
      "5481959428353082340965",
      "301664678452961755021189910649605"
    ],
    [
      "185955872790259698355045",
      "80166673732930832333554890356354309"
    ],
    [
      "2764300009111439418037",
      "14312816287352837741759700328037"
    ],
    [
      "4429634088685232111333",
      "-183383021543802975913828036792043"
    ],
    [
      "448997988298303234668663268753372835935091307102872942807130442715986477/187812125435129226643543304136867013282344265007521",
      "7067467162630810421424234083603495107154302722510136394493318674627431947430546528833272179336384350750925/2573863085894593605586438873253111369718389674624693097117914791087962691569"
    ],
    [
      "7022991167975866252123985496360215454272932304048494882785416422017963742417631581/4117212650296746488618061213077215881198695454186238965663025",
      "567833625390201179667479805732561609255257297360465117451525948581733776368869350193408767489748450956990642030371593879419/8354201532205845992280118696242727098978129865415381475163208366107868307315050336905852375"
    ],
    [
      "38996471035102341593864511355868705344090499407499/2582829038213990673603667609",
      "234119131188951852165584854488328438688270588836090068049016376076272612077/131263352080097978912184664100056559724227"
    ],
    [
      "24733100762357889992103893898306376991869697512485773/2188307592817022540454503789041",
      "3629271512934370668884403892996516749699898927345949239409868661810908442963157/3237147965563533076560144597924947876911385161"
    ],
    [
      "9104922745665790298585261842433588938672143996949/2801611008491848171992046249",
      "9341101229192903046910946025576289158524129400569877994272918400261049569/148289961645539675525430365313118925169557"
    ],
    [
      "-25731600939426697170891344435779578465593231939861160733188377/15767327105557171138354699701616394308249",
      "485718974925139356516738377277112186500462406872413195270866341129808423297341229840845229919/1979872011360748278761128371614306036741669193139055075018557"
    ],
    [
      "386970182439164492275217235670189714597265032167696877/471061030015969676898464475176769",
      "1348580980329904516152897779029784400825050776775821751442358930390474319099721973/10223880532483451780343356800164018224301763740897"
    ],
    [
      "79652164065591363052372685287972254455393704929835361657769634957178992057/48394622023878799067428817365213790271694425238089001",
      "773533138160710563770479178303909805473282964911510094875578789564858103288010958232664855800178596359157585227/10646225317180849385128787678187044481813130074793375574279658358167862761102251"
    ],
    [
      "3136500125995999844579810421909048488701108128290557363173709211166012508453/1556490053053286907544998093165320299710346207208615824",
      "82993885800915183457885205898048436606514847431141293459546767526818831987190562048519375150229396530520264962615/1941867192270076073285777814066663445157072533603535128013929825323424336935936832"
    ],
    [
      "680557613878598183324961717735367514185775053361642867714852963309013144021835086205/286770845701544451737306259067189168295338848424531721785015609",
      "34279425513513314130525680382335432496543910069016012094385160487157736413602042127868304889510455024566835591553430860603615/4856266319849592829089519335087521832855052628226667685761211956101474232482989988647974990227"
    ],
    [
      "423973301392146577038465622798511483637110190608118427941006550419466771129534894733858476720069/180501264282834588335434850234939174139936131072266431279122258487720572809",
      "26095591452910507832317599694561333274650264313707537773901285188430152969339726303825165759977112696828495018898939952790052722408581028337897/2425048184638401450678617682989683492767892766876761372851401563449163864998598224579783679794912582768772963877"
    ],
    [
      "-4624342153798435367007727484325997952077426773322399/6455807132105718179909050640689",
      "3532089655334170220860025894992836453981159757222655901566529598906531134505385/16403095786221996086312963072392250958656516137"
    ]
  ],
  "submitter": "Ritik Jain",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-01 20:02:05"
    }
  ],
  "commentary": "Specialization at T = 1547/3050 of the rank-16 fibration of X1008 given by:\r\ny^2 + (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pE + qD + pq(L-p-q),\r\nL = 66118T^2 + 260158T - 72323,\r\np = -3001T - 11,\r\nq = 204774T^2 + 267483T - 2147712,\r\nD = -264840140T^3 - 585787782T^2 + 5921807000T - 7146678,\r\nE = 22(20828652T^4 - 235127344T^3 - 915628719T^2 - 443781740T - 35163849).",
  "created_at": "2026-10-01 19:42:00",
  "updated_at": "2026-10-01 20:02:05"
}