curve #1989

y² + xy + y = x³ − x² − 44313206498368809443324946748999503935622x + 3735689660150733729775916022769811499152747824549662261493269

a-invariants

[1, -1, 1, -44313206498368809443324946748999503935622, 3735689660150733729775916022769811499152747824549662261493269]

rank (lower bound)

≥ 26

torsion subgroup

trivial

conductor (N)

7967508168203367313949873746744637648994598602284952533199954486214899069206496498166749127221983955372430

discriminant (Δ)

-459693651513865284586783080728060987123921815550690670979827873117179711630222626680477597361440297220633508370354176000000

Faltings height

22.2992

naive height

292.4692

primes of bad reduction

2, 5, 7, 17, 29, 16131949, 841863724460393869030045953389888948939694010433480424462029308358845842674145653204849703221

regulator

77393467502498993267781033763.4025907478150593390706075225963698018727625580160113439185699

submitted by

Ritik Jain

submitted at

2026-09-25 23:06:18 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:14:22 UTC

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

(815122377427432730383496560882830307741717108891706907/6944305073187427241533477512789841, -225223292985003368325393910578876760158916069389837371529423583932092310922289221/578686282383986408490667176986731305884465162220889)
(333223945610475487177, -5096082277291719298370703329189)
(832944118408120018522303/1089, -734128662906676361550813690095059493/35937)
(-112076203216437979192882637/471969, 302075239485229091695122274302048545933/324242703)
(-733788742006870471861127/3249, 276151906551285564505844490433347923/185193)
(2485597748972959587397489033/21372129, 38911231998693578412387341357351129554037/98803352367)
(146739725169787799062693/729, -33930274360839580103306056439400307/19683)
(718091108619203890623/4, 10011822055008724412330491682163/8)
(90735141328666896282637/81, 26881504934339382081631687858599019/729)
(-156680877070653988863, -2613881973061547463040696870549)
(90019932319627529410473/1024, 23617910325391084835562735184845573/32768)
(171981309794244303977, -1096100247545941487581315221989)
(271900871990736808877, 3433444994321393416586253723011)
(17223092634876179490654727/181476, 47965064263315104880794029708710889111/77308776)
(9287595964278655956473/49, -502473707301444266313239369553427/343)
(88105346802964756435083/529, 12015604063835274593595526130304837/12167)
(47516887265643059127847/361, 2937310642619062151310768134047849/6859)
(6853794282233296462892686499570150293769188868043333552701191125633/120248046192206791376123039345663457018989330209, 49252038126748734783570520904793459216978772250549802634403652858380352284244262013363659437035102077/41698174545820331094487286346823378110231823483826274879745697636990927)
(-1651265769925645599007152291040126613712476903/32864658934744310616214561, 455120856206961796339854386880413897602769711683574569455846368572149/188405551043302008000097399292226196559)
(9325842175188561421411056892183138765141031221248271954819835444013977/78645535113429289719749950734166196188445768101801, 268682008746079458750650124310194333234620381851538944458894176374323950982231206006500182847264592212711/697446834777531370175742334909553930203814030574076576901856383988011367701)
(-2920424994410211910341006356965161896901941293478785431/50009009586574556791351202871256225, 27675906783630519920739186782662327503122142714174102752712163111681809528533584427/11183361930830015152670871706799126925311177622336625)
(2672696521986021136082767940330468729689463584119212748656976453370662707326739718664664315982252599507597870277217/19124657660864117519543354449969466138505256248233800506820970135414581420997952070395632082496, 1380021780629298799031637319756481809898115543148021140374111586874979909439934861555766148439563397896224044504331850905366517209277093561919610324578757740850449492652859/2644785801758828852406003140194885469727272847187008233291932345038960525707230566942615072291759948861508026424624984434271866384567280428544)
(-1276837276824381234771416119747576807011491004127/5260493201929641150420958609, 167080918537658754688013545670922626537249144121060651835265478734577997/381539666325404876393195880111911775558727)
(266804485373333043967307178660272354019429389977/1396787655650986553298981121, 78140425985970577282178452208165643065695430125853365375031684914294869/52203014496628713907931400598562071905919)
(2330407671729713946609722859086237942987437956941705092218805388108224412322865357/45017172071694665368093877438161666521740220365261099945648016, 379715099813732650033414878412702445761075504698541814651308548980070547368789779946041958052919445952545431286736587022171/302041984084026044055663438138573961976834370563167729067492365028432434662779981763960111936)
(46337854990087914351249986510907418303039987799457553/465663769842007264837602384506944, 5608070810719209258666409625348052096471082263761232198442002291173262415057347/10048672092287970101576816862742902132653527055872)

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