Elliptic Curve Rank Leaderboard

K3 surface X1152 (NS det 1152), 2-neighbor elliptic fibration #118: E(u): y^2 = x^3 + A(u)*x + B(u), deg A = 8, deg B = 12. A(u) = (-210004115838928369565529627)*u^0+(229704902521975886120710272)*u^1+(671361220298524562480432016)*u^2+(-825066258136770176365152384)*u^3+(675067726372372360419690720)*u^4+(344099734291872947874737664)*u^5+(-3229034806631787244074342144)*u^6+(978111127560897359180587008)*u^7+(-84883145438575628808198912)*u^8; B(u) = (1382777345283637445332465597823493038646)*u^0+(-2141333171588931697572809644883683430784)*u^1+(-10798798391436050750839148859333740178096)*u^2+(14742641160489666238050313976754242805120)*u^3+(41211555355187413879811405147684931157920)*u^4+(-44965174528273847083203586237455710578176)*u^5+(-88399369682746090049036224556561108169216)*u^6+(80287083394355434332739039229066903709696)*u^7+(67485582858387264677580530489530325137920)*u^8+(-61943525190403312492725242979997278904320)*u^9+(29646663812901178376930645566762824781824)*u^10+(-5574761262185546002829095827214624751616)*u^11+(344744578091860653509920340042102562816)*u^12; Specialization u = T = -103/36 gives the listed minimal curve E0, with 17 independent rational sections specialized to the submitted points (Shioda pairing on the fibration: 17x17 integral, diag 4, det 10368, index 3). Section formulas (x_i(u), y_i(u)): [[(-10080108258453)*u^0+(17815438478184)*u^1+(33876332297944)*u^2+(-23394199654144)*u^3+(3030849147952)*u^4,(49753553200261911000)*u^0+(-27812028821294922120)*u^1+(-207353738770397240544)*u^2+(-18064297512861905440)*u^3+(162032850478238331264)*u^4+(59094214805600194560)*u^5+(-10738626096765952000)*u^6],[(-10114079969853)*u^0+(-18041207683536)*u^1+(9773675048344104/169)*u^2+(-233552800545216/169)*u^3+(-723222560801360/169)*u^4,(49720819221642254400)*u^0+(-812148566894649776880/13)*u^1+(-3910026452032971237744/13)*u^2+(971878286242884652895808/2197)*u^3+(124771389780554914089024/2197)*u^4+(-425487495033661902605568/2197)*u^5+(55127822923228129851392/2197)*u^6],[(-10211690186658)*u^0+(19053319485528)*u^1+(32208238897380)*u^2+(-25547714357904)*u^3+(5790774069552)*u^4,(-49622710422611232270)*u^0+(25469412856432875846)*u^1+(219012328920022391916)*u^2+(11167380659183666040)*u^3+(-196834385597398478352)*u^4+(-22679768978861618880)*u^5+(6883884071338982400)*u^6],[(-1036582105869)*u^0+(-5439167519328)*u^1+(10762460049960)*u^2+(4471942854528)*u^3+(12798081782832)*u^4,(-39991874723449442640)*u^0+(15687271511145504864)*u^1+(191384899048735843248)*u^2+(-96172978953858924096)*u^3+(-221811111873415038528)*u^4+(119018729616601231872)*u^5+(36805059977813729280)*u^6],[(-10378833990813)*u^0+(-36628014643488)*u^1+(120779033553432)*u^2+(-32082552167904)*u^3+(-1100601991248)*u^4,(-49440521634671550240)*u^0+(87682115251697088672)*u^1+(626760091152730298016)*u^2+(-1408418261085193738272)*u^3+(496483071857128485504)*u^4+(96757910616374455680)*u^5+(-20900572972064755200)*u^6],[(-10504255326525)*u^0+(-376816162752)*u^1+(43233929241336)*u^2+(-17215712091648)*u^3+(6871270155312)*u^4,(-49291796254101500736)*u^0+(46659003193004480640)*u^1+(151010219282731514496)*u^2+(-181965463537307488704)*u^3+(48514484588765898240)*u^4+(-9113408660123698176)*u^5+(-9268879791137218560)*u^6],[(-10614249506093)*u^0+(-29218788720512/3)*u^1+(117764810210552/3)*u^2+(95434591907968/27)*u^3+(-62446118913488/81)*u^4,(-49152698244932922640)*u^0+(59264078619311854912)*u^1+(661333908853560905200/3)*u^2+(-6516624318252378189248/27)*u^3+(-3695939059750605830720/27)*u^4+(13250540893078110479872/81)*u^5+(-14756194666576013593600/729)*u^6],[(-1071363786453)*u^0+(-21381180297336)*u^1+(51924681414360)*u^2+(-9911458355328)*u^3+(3623363679792)*u^4,(40081646882698785000)*u^0+(25311833141056574760)*u^1+(-365068021284392325408)*u^2+(387833030441934942240)*u^3+(-21943442681307812736)*u^4+(-85800067366988911104)*u^5+(9206104486232586240)*u^6],[(-11271974814333)*u^0+(-10090436343552)*u^1+(42113920079736)*u^2+(5601317962752)*u^3+(-1131694783440)*u^4,(48143020827292110720)*u^0+(-6706810337925070