curve #3427

y² + xy = x³ − 7652251054419057114417387759487687195044258065x + 258496580779691678509249287746824300190813123595900095819873473260201

a-invariants: [1, 0, 0, -7652251054419057114417387759487687195044258065, 258496580779691678509249287746824300190813123595900095819873473260201]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 81897856783145083322089400705546329231078290770539472432906202060246859873264312354790507056412940535842
discriminant (Δ): -188531331419112989598084768554780077748723255738014800473160384838645207923096343405176185654157993311177260110526060840394312714890149888
Faltings height: 25.1998
naive height: 328.5741
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 31, 37, 47, 67, 127, 347, 1222237708243874998397113870625886646773801370784237074755250535293911252624402236011
regulator: 4954192823397870929045338921.63720979519659790937665480224023173262340989538884567244599119
submitted by: Ritik Jain
submitted at: 2026-09-27 03:33:13 UTC
last updated: 2026-09-27 03:33:13 UTC

Witness: 26 independent points log in to add more points →

(-98793620225204296167740, 7088491279641951608936820482670769)
(307774362662861598828856606103469730423764266551603400781226/7222662075081389480776143238145726209, 60741848410785603929342747261700171466401805813498589563415523252681044098005068124943867/19410912154239085981862515879241508608392737367948354177)
(5099448617573124024607450/169, -16303582572594348195865577104147214153/2197)
(237271420724725268518706224/2809, 2181930049864557336057936668379057624281/148877)
(-87935488112054521261284065/1156, 786497754473498468080914641099583658309/39304)
(346252392003684768374784602200/693889, 200806053587107833070021463055352622619044963/578009537)
(-13084079198178748846908, -18878011949588354273429871899898741)
(-14793918742922263252183394/3721, -3857725482123843565001037937932499689857/226981)
(1267512889689912025055146/25, 115334154036318511566383786281438991/125)
(9052928669236945424868850/169, -3328621335698417635180634727244049753/2197)
(1426935185614716446936854588/27889, -4447281665824525456802384425053431517523/4657463)
(1635846722914135249199014, 2089319846636636160952985634622918915)
(12229866911499327587987635270/249001, -132387973006931963117209444263545206744991/124251499)
(18997869399260284484165626/361, 8502102815497884466541511870333479977/6859)
(-585976875534646122413234/25, -2576883620301617752539060740042765401/125)
(2056065974291358498127578965149806634/41667631772209, -275348650140262165651555623493094689554920030772104531/268966521468302388823)
(1672609527109016812136164429719316/86979575929, -279192358570994901496547166220104194591451890429485/25652277471708467)
(-71741798307026888360847832595411529994913986559/87966568704996876335751424, 13424054559807171441429633421037630069385748363847522580227131808172613735/825042798391159274761967517109981868032)
(-15350386128734609275277218834886235460066201065494/238292520778198733052789025, 80936416465864834664332241261013635307441354961563968743243741869923522069/3678456437386890926864917959481792007375)
(21282277901395485994240387907088265505117810776888037011/1805771321841973929903923170415236, 1000346046824762167159584045232269319865526542655341724315662440696205055768250188173/76735111289274959837831015030830138457425540177016)
(3099484268560942831797441353483674882930/76131648289568881, 79813912852624240462562966143271109666975968869274926584539/21006217064796109690291721)
(-17031780496901572323718919039165527215631025806667678955272/896969113193100604165672163070502441, 16925265408989523280946478837630469950486336914890259590626319166762263438452223357900577/849505573942121407327696775958181842841672095707677739)
(9072216891078494534839745920315687559064382252329844560639610321662888182370274566103954057314333965714355490196851/123048464093169333007352183100477146430645944184683215638471292373182138003871655461044721796, 13310141582387359015531276297403997582619955430666706848483745825879775499443424412899135787515325284250893036363226741896734721121078267267031710751725127831256910866715343/1364942308892950979303791780321190344843660482104001141226769938191278453600841623314060577220174244701130939654716627024993105024680203656)
(2553155172923535166177937208843528646554712697884768250547687265745220808984/49686889854226634141534763434894180723990691234407329, 10871591576342004766423044851328323518078457416965068146127231648008703105868677056636396048795159499128743320717/11075484138606613599443068708772476264464913149838910305206087655456894459626767)
(72688264664918707555816838733230164234948450850982473016070446017495284/4543764012480539257410667002609676788797784338449, 114672279146756650979692312689465034592596926313564677285625380031511472955160698111695739938175789466145683/9685535812620722320141090894106487153297611840000540683457293995810364793)
(1177138382087247221005778620130777017024883879512666/20802135927851104691251662025, 7752100661082444537140026492687338644992319997913773415960108408928443915321/3000280744891512331055429656972712882858875)

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