curve #384

y² + xy + y = x³ + x² − 65838560278746184445004976255x + 7804621801493663292406561910967222627057125

a-invariants: [1, 1, 1, -65838560278746184445004976255, 7804621801493663292406561910967222627057125]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 2655765272494226177268820739459919812784634577911133531065548202468540290
naive height: 211.0497
Faltings height: 15.5850
discriminant (Δ): -8048982908040164938257367514212363435923458637934622402798571165236429219655936000000000
primes of bad reduction: 2, 3, 5, 19, 31, 67, 12227773160766244165661, 183455595269402303884621034177205538329569101
regulator: 595536093681764326716.88502661160936896600136488837818747531783633313749582
submitted by: y011d4
submitted at: 2026-08-27 02:22:58 UTC
last updated: 2026-08-28 17:14:25 UTC

(101487980990601023693/591361, -568018477947791020671804028728/454756609)
(-52686597949864717/196, 6765458898257039930822487/2744)
(1063401033495427187/9409, -1226933736372021264285196206/912673)
(-49985467624134768917/2588881, 12544076710246961378525582830962/4165509529)
(13052271261673431803/25921, -42215457755340930857765518782/4173281)
(-7168242859341288013/24649, -5940867805248234725770556406/3869893)
(8512954298368601/25, -623365028356595020972164/125)
(117844122276707170283/707281, -718793711856484613951932123662/594823321)
(-97603974403170637/361, 16577214197389104154632342/6859)
(1748218951445582537/2809, 2146582500625902076765090506/148877)
(192514846663903, -1504892186151021856682)
(-24331237371336557/81, -503654916618570170046878/729)
(232559224659743, -2251875386165917853622)
(7292079426902268403/44521, 11174198553230262725853612118/9393931)
(-8118392176103701/121, -4595318917848617966683650/1331)
(13925944870208099597/49729, 37324326260246397209080992726/11089567)
(-77640329297757, 3528219389606887726378)
(-71859358231507, 3487789232695038366378)

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last edited by y011d4 at 2026-08-27 02:26:09 UTC · history