curve #1855

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y² + xy = x³ − 4586159601547448028614390345367325x + 119013973009882384417345161045995396616701435414321

a-invariants

[1, 0, 0, -4586159601547448028614390345367325, 119013973009882384417345161045995396616701435414321]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

125832909343457811577797849019949409633015447879422431920938096809444498254576678

discriminant (Δ)

54454616205873870516795888535680057711122674329303883789928246009067363867618721731535024161369096192

Faltings height

18.1757

naive height

244.1387

primes of bad reduction

2, 3, 13, 19, 23, 29, 47, 83, 3614031542039, 742172200684373, 367177063541153057, 33133863902342600529033203

regulator

43713032880984949153505.8713594567300498894776567148005682671933274518782245484825114

submitted by

Ritik Jain

submitted at

2026-09-25 17:14:17 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:17:51 UTC

Witness: 23 independent points log in to add more points →

(2007104426259420527290575870864352692835765490/1888371235986617328400955281, -89741481816007407920731926268305953232851560122380029019128966958999/82059915389110184624297449001102788324679)
(1909063257491468672770/23409, -60717175924741871632157935649177/3581577)
(-1952190023277739846/25, -123963524095052754257655077/125)
(102024946378158830986082/2436721, -2386005417437422783817880808336441/3803721481)
(1627404687525848997266/60025, 56197224278210565639565532071651/14706125)
(-380700825576656456410/5329, -3523744200405082913120717511697/389017)
(16886444114366922888410/499849, -573747252691836231082632998545883/353393243)
(-7215632762751916477726/108241, -403676715319064305703230269889385/35611289)
(1592551205455075556542/2601, -63180237588052494809956958919011/132651)
(61002097049374838170/729, -352752155703929816066926537883/19683)
(809248498988589376784/17689, -5235637889692760200862850425179/2352637)
(53242847322497446286/361, -353143279734014916254189517031/6859)
(-4634341353938772160774/1500625, 21211692550499107063982714792786351/1838265625)
(5772518584774949389202/182329, -183427713622793883607377718345411/77854483)
(-1883983234942026094/25, -756803549391133879872144269/125)
(-88335951247988211064/2401, -1814787060664885447606563803833/117649)
(1166215985560058167424838886583090/33109931802054409, 6532944914461380556509814989614073615594665627957/6024727789779957628928923)
(98060980440002908322/2809, 179681744180283582534835204531/148877)
(432015859807120354082/12769, 2316698277961839787536120816031/1442897)
(133774897889207807/4, 13952931889219240500423037/8)
(118648609597194644, 35286646588903527719563295)
(34335297501700592, 1423072511654084689484969)
(241543973578505942, 114471714505754667819974759)

Commentary

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