curve #2092

y² + xy = x³ − 1805673781082257813668146649547176789832690x + 933548448416981135012112176843191800549130430151103139827593092

a-invariants: [1, 0, 0, -1805673781082257813668146649547176789832690, 933548448416981135012112176843191800549130430151103139827593092]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/6ℤ
conductor (N): 849008053912545857392884883884697738710
discriminant (Δ): 295194114396658836448146318488648999210983879584012398177262412995587078624597825037521189765809176684788695171875000000000000
Faltings height: 23.0330
naive height: 303.5121
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 29, 31, 41, 67, 73, 131, 137, 181, 271, 373, 509, 1123, 3319, 7489
regulator: 849834853783.23221828042985090288941997739299102610412179
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:55:24 UTC
last updated: 2026-09-26 06:55:24 UTC

(796646073193227442124, -808047791778495128239041318562)
(16160069044018171543391176/20449, -1024661503604872661019012395476687834/2924207)
(7759896576106741372124, 673937385136713388148293112561438)
(13411026652258434847802996/16129, 5427021733132122238066053686292634754/2048383)
(10631484888485173306866356/12769, -3904379199988985498699547856409324114/1442897)
(203838648477263669643146324/160801, 1683447581527773742223415071971508537038/64481201)
(319365080873982128174562836/339889, 1615601607279114515673070758078533943506/198155287)
(8575790276837580585900438928916/475370809, 25045966952519088078109917805126932038092654426/10364509748627)
(43586387803166295950574448436/3485689, 9049173843062569135067501558764836842509994/6507781363)

2-isogenous partner of curve#1910 (Voznyy (2020)).

last edited by Steps Unbounded at 2026-09-26 21:46:03 UTC · history