13502.txt

Saturation index bound = 3403
WARNING: saturation at primes p > 1000 will not be done;  
points may be unsaturated at primes between 1000 and index bound
Failed to saturate MW basis at primes [ ]
*** saturation possibly incomplete at primes [ ]
Elliptic curve has rank 4
Torsion order is 6

1 of 4 generators lie on the non-identity component

Points to search ~ volume of ellipsoid = 105756
Points returned = 105775

Solution found - (1, 8, -7, 9), h = 2028.09331273663
h = 2028.09331273663, lower bound 1292.05926831866 digits

Smallest solution:

a > 0? = True
b > 0? = True
c > 0? = True
a = 385237239964436003717966934132007903609313924934483451423693857070687301348103308586464192149494491222189959329858689729486830871440625856164622553850193044277371161914140270588378118924065472701360876320271530593623343460028492568156007084397247457699617031296796211274551875017873209856713977191795362049414062599745203620185083417035998108113613318647242172900184059643366161538379112142250412446505327334861262256930602213750324075320870195694706065771632872867931515279250803762850022392152631352678036662865939218063150636310870227408088109424976005472325216341032011358974308704598162603436807382792431450058722488279320393514032557911261843684155909788168985520542352543633634685091532795077060090402873212836328376806958639081204806254377848720914584640262745301842245922487941057415827332063234033973760432393439062532457133585797975212251893604477917037341039942765634037025594878460043080058062652563548355364751698094335625475265314257033421659000673533493682242642307930391892561704153326283081928552658339104558869516987150034417875867147009424898584466576388035415671698001994432051571823654281611563416370230783152933861629702044051888183952637623917861280734045438091369526929254762618359584088000254158253496697614325525908279385577533267318614143362638562144860561197456569216959885702047132807255
b = 472672968140084458032001470504533956598785905737479431494811528150330492288045278306496665414229421421704270726730600971198230965104794075648535467181432641302900150840434717944327574917113184193222529983877098863084433827349802523511286971929622739697988474230961796880412909261819445197807243066520143033591503939766204511130871061010108052106725605795013382660118366671680910839564067484563577356553401162233648477170774868043753200737214260810993918062659906489793284908555909442313791215531356577140652611277074884753505717653995290232369568616702601578508604799308943137406453831246406115298064487646461078582761498033165340087707883870950786407810582462762039704782443825301760212080536639055114295770700624820225220220323192825091200492260966787407093332489854493813308101458308725786200012868882770058316282602060268033079585684319551922759855413862743240360355793951161383919688844192134115056353814986574762213371653414098297206350643716926871884329285520880470090249850211978687061288608065062192652518695377875022815294196392911994994308179456021452545592168400657904631492767296254626574577588913767069618554037193959145401893443787781209681382470663355761497560069896558203088484364353034100240067775670929635807213459694839406141673440939111406599876431142851117861499002480313886682028591202737599269
c = 11583503566290072319129413150820546875976188741034399680252817436966930212877236591978328848360414351241408095858740483821508432868137979266562588112485760875510550697241960486654568112627067880110939027199913771535339161974538332941511454059801788882234509603099795894321486386726433149348152489276858077258800933907166158391395720579170036549704742187679776640930225923796910359094152010016506520666978120854945331990220550088819874875253930487510405475649735358824042760663533040616576999242012740423441828204040158171829292937113244044305072293663376511982459935731954116562994944332331478687273236825952361127868199792559474138579067834166947475851563689739000190366797132720999626529585393104512268940149939016086328262522037945321769736146404366087800502425421021635571989445861104376983514023532002787356850034483731004856560853722559463850395090899554540677168864549925437543699640668921625695086161058659548522642095934673492752612105876510039133159974802414647863993098938329020247834056292921665139212359360683946692276170060013596489559669094461421593918844562788150264814015001615692003022548210426737113836288433326901020483126664683244095375243676494307739505687793186888223965917958676050973060995295486563197439550739162369991254747225942894365596921476914335074263485281585144432579942791769050946867701

max 1322 digits

a/(b+c) + b/(a+c) + c/(a+b) = 13502