curve #809

y² + xy + y = x³ − x² − 70395983486685495363860335953529345211001957273585324287x + 227350395474899697384062335490304356424681441731630349492030142716154034141197692199

a-invariants

[1, -1, 1, -70395983486685495363860335953529345211001957273585324287, 227350395474899697384062335490304356424681441731630349492030142716154034141197692199]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

1851026262599022238420132548888187068030081720818041403734048112592380790867403361013489827290344302881442476501565422616251625911710

discriminant (Δ)

-2650733971038717794495469945821888703672126377870411841278459541168072162745325928069425338947409485534931076472329073930252518012972216659043948155783342775808000000

Faltings height

30.7958

naive height

397.3949

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 29, 41, 61, 127, 157, 1381, 144581960246343431420557682791044883697, 4185662643750969273245074424076831560919634604217275474054680617024391652621

regulator

22024166378507032517233459015688628.9713980951889841343094216859723450449928903503876727595153835

submitted by

FNacc

submitted at

2026-09-20 23:17:37 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-21 01:54:03 UTC

Witness: 29 independent points log in to add more points →

(4886802118405316448262302307, -6330011119161386259768474609295757724154)
(4777299079232118043589747327, 8834580822462629051195660512661859857146)
(4976362597420004545011800107, -16432247102047576151481813800965911733954)
(4853291910458959973956443827, -3837041929146151647905228874571753078474)
(4875563235065198398735994117, -5282982653792914181190392610154381809854)
(4853829145886168954960272747, -3856257211702310824007866401948882324994)
(6840483587583963996522892459, 256688935108346085797788546433845713744062)
(5077221027672485015845053097, -28564168296812501103056996414382697010254)
(5108443114895164235593362707, -32363959150705760473811680410555308634154)
(41983377832190974369240933963/9, -588348211616682680418236035587115264206158/27)
(7027624982438521519198932307, 282330909915065148994624253265556281101846)
(7011086586047216601660778447/4, 2645414949020989461899915447197835640425419/8)
(4823128893051915717219709117, 4458502428203845526989210372016966790146)
(4124826139253285723657662099, -84615489963912157344320648282882164529578)
(677649440695302397599906193, 424214308104240953622249201734881573131698)
(128431364814919108821156227, 467238120944976826251350761401289183025126)
(-1394075097002279482782196123, 568135876513261930163350861364266050743896)
(209316896175383410769648055495913/38809, 516612504994179437273055030620192694268377613708/7645373)
(1906181988903101437510858454977/361, -366895356408457366267070668880743965757636036/6859)
(5474126667541503711269783587, 77665232412148491796390359769554627882566)
(649781390560659859131848429863/9, 520392776805106913312141749520701922405995342/27)
(1398216381376793852807724515587/81, 1486121640215295710190401506457669612677958054/729)
(707665397049775418134430292307, 595266652075190172864817349151585568949261846)
(589445652177854368174015551467/121, 6572672357880885451188381751908452824884706/1331)
(342896688071263819295925342517867/62001, -1308496623521285654863412733107844507263314433146/15438249)
(304091191103157949325506456646867/63001, 66822019491487280633194599545484654739924382146/15813251)
(163539482182400933197850681974027/32761, -108394086268260677297568179817799980122672374114/5929741)
(266221449837124374240347345677/16, 122481400046467372471814772825049479090307859/64)
(1734788301058266317495839807, 332338826658315190203520459888447358771846)

Commentary

No commentary yet.