curve #4116

y² + xy + y = x³ − x² − 16810591558483433700206213637862543359222299069578680898640x + 838477396033762280244371312525319269741149799848099002341300486565412890721727321492787

a-invariants: [1, -1, 1, -16810591558483433700206213637862543359222299069578680898640, 838477396033762280244371312525319269741149799848099002341300486565412890721727321492787]
c-invariants: [806908394807204817609898254617402081242670355339776683134705, -724444470173170610131136814018244761279721005389512995877105311026924720984543410695662025]
rank (lower bound): ≥ 21
torsion subgroup: ℤ/2ℤ
conductor (N): 2354821899258314703620981481029366760380391230269986226723630380510794423225946002025617184809098350
discriminant (Δ): 323610868047670245388783279137529604237415321245537868064205715893679576499201238736000737480114059015958918259905599181218593503120650490498064718235231440083215013189984000
Faltings height: 32.2360
naive height: 413.8217
primes of bad reduction: 2, 3, 5, 7, 13, 23, 29, 31, 43, 61, 71, 89, 157, 229, 359, 577, 719, 751, 1543, 1951, 2063, 3331, 3547, 3583, 3659, 3931, 4421, 7877, 13151, 99079, 114769, 467827, 1516909, 2985617
regulator: 141945389925586473730606587.21897237619736510519278970898840197437807798133590241
submitted by: wgxli
submitted at: 2026-10-09 15:31:29 UTC
last updated: 2026-10-09 15:31:29 UTC

Witness: 21 independent points log in to add more points →

(73426584610075718753670557873, 99049523964453226143055343002210412539845)
(73437414446265653096322202629, 54283387924437286298858779935146838217985)
(76353239701791280373002183385, 244336486571057836373310945120179799348813)
(5022408909446323452668129669, 27462236242324138933812671260305967202261505)
(69508615359490025674130348219, 2413231635506234486079947638458292279597755)
(70252314796519319229816181385, 2053494266424194910930903665966278162544313)
(71118801483896372967340763879, 1624473734671549744646372523400736674416135)
(80857710101745140598491015969, 2802977361616413101043160353786858673377525)
(81489467334507132136611790019, 3118455496846685706608471717592249803878755)
(-25519995935725430956800446781, 35367544608245347590477151534307732061330275)
(122627253549190579558014117089, 24920696149118758486477543583477975337484725)
(154370447118014145194747944055, 43841793804254229736000500914634243092301783)
(620581410762548127077197863845, 478962679767839199211859636982131689374717081)
(626069389287591509643740150853, 485499579441125011870699949509986903216424065)
(-1346875510660664794579524889175/9, 43616064642502402213209423761878540085678167/27)
(2506684775743464081599264123435/4, 3889744963498221200295517227390282281902326669/8)
(3884624549264675635912745604437/49, 688546901909445882317881482428815131673980183/343)
(-7326716748874212649002313898155/49, 1031890771329865526532002050769864158307842623/343)
(27795340313494064273598885382359/361, 5270113464360739943038899628469548196412281525/6859)
(-511567173695987465274235120067791/3481, 2386636424313917853561034150699746449974059682215/205379)
(55886508430157245485368980485060865/356409, 9652515739268251760359343255187204886735252125627973/212776173)

Commentary

2-isogenous to curve #4115

last edited by wgxli at 2026-10-09 15:31:30 UTC · history