curve #726

y² + xy = x³ − 482796508985332347545893318704380316582591793909730x + 3870122176786980555176119286085226447895262973944708132601872961243808376900

a-invariants: [1, 0, 0, -482796508985332347545893318704380316582591793909730, 3870122176786980555176119286085226447895262973944708132601872961243808376900]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 1061156481505838010850183923903797195582912882706332006180233814038630064593061708858616739945348222391528179801290
naive height: 361.7246
Faltings height: 28.0853
discriminant (Δ): 731889415658782039809006814955691634867839462565194279056914110340188896112043705712562235489645828885336422980400377053950338033241050885612087808000000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 31, 47, 53, 101, 137, 223, 673, 11597735724461879396315170812308052975073894195203996501698211735377356800049779904075963241759
regulator: 198767079612842167834810936413774.2407717834853098431178736728684926549835695386022712054822403
submitted by: FNacc
submitted at: 2026-09-13 15:50:42 UTC
last updated: 2026-09-13 15:50:42 UTC

Witness: 28 independent points log in to add more points →

(61685000453496597116322019/4, 76816815046515313515674506329587365751/8)
(16213033686124154495255692, 17444886157802503172542499900082904966)
(641627263407184510251837730, 16243237498618923558896466433246382800450)
(5776838483765013917329885860, -439068418951560839338286794836544988778930)
(-18317579594970487969647920, 81040853862572249726906443734420102850)
(355812696756975213456540430, 6699173401580796615543504482171939078320)
(-19047041939683032866125340, 78459511017936304510656311031508053070)
(-153770224402550124441020, 62804126205004450970890283310810693070)
(77777109661310470676359552, -660919832326533396362514427004958013358)
(576272599639771091223640372, 13823895189345290214140011453909590102286)
(759845479251614585668660, 59192145934548204805670494403044173070)
(-12214954639216582837936664, 89134313818525549780265526586630589962)
(19924365158290069692499336, 46478911665836612960535136023578281102)
(5334371948482525177527460, 38032859107451116682876072690152115470)
(16598647130016745462523409763/4, 2138469014966574510856650868881966971603363/8)
(-5064615909319121124907887860/289, 409548574808608086150641525477568619711910/4913)
(-19392087912297154850111478747740/5583769, -978967151505461036812813482225224358064081373110/13194446147)
(-19600640133454375084130990, 76177221280378551487218803869424139820)
(-20745948301598111256199340, 70407771046412314694061995888641533070)
(1456316547946402315382557795240/78961, -781148540588324122241996433132761212026137830/22188041)
(10014176346752350370411039740, 1002124795122672065032142360530450633510870)
(5740505877989692905435446560/121, -394268832761335869666762709158813713663830/1331)
(85203669093485921352844060, -762419964268977769715470184633686909130)
(828916119992972935598405860, -23856939063322375114825566375886218458930)
(1070278160890893009360313060, -35006939185893417790378314768398825114930)
(154751221891045660527461932842049/1537600, -1882393019164728712452185012045715753249728012387/1906624000)
(14983427701506074567745040, 40529981161654461649343091028724590)
(1832794537362449237873226625162/185761, -655879219974323296830649420178323815062935828/80062991)

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last edited by FNacc at 2026-09-13 15:51:27 UTC · history