curve #1677

y² + xy = x³ − 7361352324983048088678111151977763311585181188x + 243990215224550312487014065098143421886858015737984837693495887576592

a-invariants

[1, 0, 0, -7361352324983048088678111151977763311585181188, 243990215224550312487014065098143421886858015737984837693495887576592]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

101376256245105340964767638186502829488636494478626649371283652035614376862879389493617955234108114105620399219650

discriminant (Δ)

-187373344238225155205362228497376101216576374312921318788656213705625321395155720765953411121287526813986687114598412946636622848542720000

Faltings height

25.1945

naive height

328.4586

primes of bad reduction

2, 3, 5, 7, 11, 17, 19, 23, 31, 89, 2259144926531058363447311317, 189551887636872774995135362742202519366429239973044915833417532824951429969

regulator

1197652505753154747061657775156.1040038274864023173358628566972060880911298328911184054031684

submitted by

Ritik Jain

submitted at

2026-09-25 04:08:32 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 05:29:50 UTC

Witness: 27 independent points log in to add more points →

(4920109960202053752142572391150869072/83195176657321, 2985833443278560968891636758401381089162669122440602236/758834770420980208619)
(11058776645273702937162857517/126736, -735904912241534624533095570111894276679461/45118016)
(-464414949002801828941927837908/6145441, 292532784606031809793363258382041610952312276/15234548239)
(36058062428392491179504944/9, 216473528535160578281549826217050952660/27)
(-105380684754469914550824075271747068455141966999778071361268512/6784727617301749103539035921789364846129, -10523392499629551193112738992274270928657322114150458108916800792715394959698738105787043399292/558854336765508512924526143565215065237919779127968235336617)
(1478860111238650093449628/9, 1590715864542254894089547065684461128/27)
(8481337339797285081762, 13496895629090939128130303804270454)
(71079253381064894447308728/289, -566832195376968712740395322393426702468/4913)
(-16089362332396723924488, 18927880645834958227557772742260284)
(48270572852347190116992, 1061264851879872472901969119403844)
(4868482714015687202299815768/97969, -28996736098800919431795608706592417498212/30664297)
(16777200202698852802720508448/97969, 1940722941169026263064750524741079307052868/30664297)
(19608302382179248467642, -10353052751617332416302761010427106)
(185305246843794209953308952068/4765489, -42309014636792849128324684143544072110660492/10403062487)
(11734352855594373888920705988/97969, -1008023016161233595305767623303589278502192/30664297)
(1827291908550690087916872, 2467410081600858633481840748469481404)
(1682609641820407275339144/25, -913610044911505323769708247578172532/125)
(-46706519413770537810192, 22043664331870920484684822253803092)
(-201185490792693895731011895753/5635876, 287359270455325853697593953479737845880953971/13379569624)
(314698021977603817007969876934/16785409, 729632323929320395294436549004992481556080162/68769820673)
(136934010822531304831382639508/579121, 47717478158114659340326464856088763690302592/440711081)
(-12933871783136218171668930125652853461853368/132338224929966141529, 8325642417402493053510136814367040407459484865625440739387304500/1522397133827994106838577842083)
(2582807642406491814660894712884858238723964104/162759934894570682068449, 752036774151964250171590185119415624618219689850538484971245632779460/65663081701134856098082917350220207)
(-9339101634699891863692793938915250181343665196304059723273/96562103839281392450587744027601764, 214854265591815605622321844627096738675888771087509523947491986334471713168419084488465/30006136393083265575706608182363428883506103738874088)
(30021371573060081238552, 7074607138195577706958516849882284)
(9307440633976796992259832764992932/4091009521, 897306622355866360589894105097079009339022715078384/261665059972681)
(-182505419892217050888931104471160038990007902/7125352696909141671001, 12263619712695700114688773744429009726184880943410721391499485038770/601463877070829399464963455225251)

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