curve #3832

y² = x³ + x² − 106569315573931028048580986799243379745x + 419647868987933919371121442137490921142154073778336309475

a-invariants: [0, 1, 0, -106569315573931028048580986799243379745, 419647868987933919371121442137490921142154073778336309475]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 17017644300946904962230570591242485880534696930722865713740213827250693014309694750360
discriminant (Δ): 1382751359187986386684445002061299093673715225998814246064644519127841783607222638123595020313121744924082580000000
Faltings height: 20.7187
naive height: 274.2992
primes of bad reduction: 2, 3, 5, 7, 23, 29, 41, 47, 53, 59, 73, 1477744798720698975165515801, 2031583095414710056018082338665776575264007
regulator: 392818504036211692793203.21488737523885713607395128919221874040781524831632114019401976
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:26 UTC
last updated: 2026-10-03 05:22:26 UTC

(-645214192781926221, 22093874725109877535348259610)
(838429538470340372694265/104329, 305587430256604379793839283697670250/33698267)
(21913135587762507085/4, -3943100897490404473897822035/8)
(3687771292107511095, -8763391549017847118516628510)
(5170088302972356910, 2621181208591914697034022375)
(7402667034553617745/16, 1231797735382582341062559747585/64)
(7076669952845237935, 4459414002029597797750742850)
(98582967845666022625, -973654103105373688402612830510)
(1971991161706979441473/361, 4882212220649956339305063696126/6859)
(5488802432985050110, -266155282564100548269896175)
(27079451483124349142590/5041, -529408332943966530842550582523095/357911)
(19340404566635984035, -74785404136558217391218427750)
(4787154335863249573915/169, -311707001307905541688505583750750/2197)
(1562748436395450529, -16028828867528078317476197010)
(56537607167078758670095/8649, -1231345339629918373657006285813910/804357)
(925539878774203926505/169, -1144485711392151157723707276570/2197)
(-6202220164936168597865/961, -862711550437759172751167979113250/29791)
(48610955092577400595/9, 34305439225627297469805053410/27)
(6451770208560197935, 802654700180273381320617150)
(5479231168321403575, 476749679930238802015902690)
(49314960388867368190/9, 12774276972809960156389673875/27)
(252609550499931891235/49, -924458190526227253612045765590/343)
(6427716541469669083, 463784363886049088293527354)
(56709267262035553741/4, 335463315621372942214611042195/8)

X1008; T=-422/421; 2-neighbor step: yes (Q has vector q=[-2,4,-2,3,-3,1,-1,1,-1,0,3,-2,-1,2,2,0,3] in source section basis; h(Q)=12).

last edited by 7fff-zip at 2026-10-03 05:22:26 UTC · history