curve #541

y² + xy = x³ − 208646296854590248743781589057746919818075x + 35169420298107415528201890683292524212433613273889868358027857

a-invariants: [1, 0, 0, -208646296854590248743781589057746919818075, 35169420298107415528201890683292524212433613273889868358027857]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 61669146862423542217392777244878590537129695780711417978557437190143686192006044234783857924818170
discriminant (Δ): 46979983242636040722970331564759175266930580036806335587635036404205180232736278978688507373352648971041154811479688192000000
Faltings height: 22.6833
naive height: 297.0380
primes of bad reduction: 2, 3, 5, 11, 13, 23, 89, 101, 20947, 303493, 229589799727, 662439855953, 975468193729, 6701871225201503403188571567945869059571861
regulator: 491185533692393353692899403.4027481986441047691420127168615090226535533016905772997251375
submitted by: wgxli
submitted at: 2026-09-02 22:39:38 UTC
last updated: 2026-09-02 22:39:38 UTC

Witness: 25 independent points log in to add more points →

(-233224570630151713592441986970810386/868394790794521, 216890119832451913515531902694279919673436791690969747/25590325759925183074819)
(-239367057497722271866, -8449707374001358260630077472487)
(17087258556886513998206/49, -752768460070613704892127391079641/343)
(-274605662211376403326, -8470970249576568223569621403867)
(113582000868905981644996140686/527023849, 5582787175739129340317833601696382434578469/12098886501493)
(550920777207797487722, 9350606680084197219848094115913)
(1306474833954478077614, -44638206342396068454792626477167)
(147967248839654528294, 2745221685677383206468461262113)
(1362294805446925385864, 47740366234662398757481334650553)
(-136169792832391245346, 7813824549159558381186579293873)
(-508831564656212845906, -3097399693253490153352172241007)
(371366148891740882591639444846/197599249, 220141070041785820914350770815680216572396489/2777652643193)
(373558896180201798097564334/1207801, -628032739778695660663093125263973475453/1327373299)
(148373336917148372204, -2734640680464008926840174966477)
(3383043160238469233357693396246/767123809, -6190263170183229858962756478321953224467236911/21247028137873)
(139512290919797087780894/961, 83939833298288002746487131596330543/29791)
(1203737377801646280986/25, -627928575998841951282146533957031/125)
(248523221768864432279393736927388435592087/9195135885019276516, 123876469204577779227461426494292480344822374066869968814089723/27882854172669860819481590936)
(76706610599679750103113774741540839383534/2753269960935321, -21244630879981868764941303772104123123357396659878524107643437/144468510368183359672131)
(63329359219287549288481120473128437061051055278/20473045258513727595244369, 15771894626350587521911339886474805630673843597785101414923547161593385/92634693681198325680557846759604619097)
(288076362196158356849453913620355110471723001914/50229534660450130768661641, 154141777016854893070038601890525271475699493917452720331602108084568353/355990765288550849198330775590934577061)
(49574985643602003793183295344807060834049/561133754620795456, -11037941856889682931904030248397293598317125438100543872756317/420338907639775272954128896)
(26497854446369232308181215770786371624902/53960808213223930561, 2834208531346364230364915610363268823815651971606856717509625/396385417265142240833993297441)
(183722806986803845644252957070688726/208376817879169, 69678872282549325306216187280454784371898780806412031/3007974169188906736447)
(248593532256494748969941379860558/335137945921, 3295590254395648748388301539394307825091654894911/194015043411072031)

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