curve #3819

y² + xy = x³ − 1918373892861175434057540733277523501795510100005x + 1011474301335459950487010919169289173157435113767620140299194158622289025

a-invariants: [1, 0, 0, -1918373892861175434057540733277523501795510100005, 1011474301335459950487010919169289173157435113767620140299194158622289025]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 2457128491390343942190362213360631887302792806948065797892961946841231980199678863229387616713338836257370
discriminant (Δ): 9864192774037416482738812873781961363237114387113211361537053311686789308296007094596780345914793920290084720493773312872611051942523037440000000
Faltings height: 26.6309
naive height: 345.1403
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 23, 29, 71, 79, 449, 1055626875044636412272773846100391000533179112688638929226014450470438766608782522829205813
regulator: 38574834479104695869284499278.984965757746429688436673581661177694080525462849273794498884398
submitted by: 7fff-zip
submitted at: 2026-10-03 04:59:32 UTC
last updated: 2026-10-03 04:59:32 UTC

Witness: 27 independent points log in to add more points →

(30785016520614319387911090/49, 79863390238301389904447109822181789185/343)
(869020205671806342311610, -25481602700506608097072239601456905)
(-5100069079290690076714110/49, 377302639830775547048560241411755167585/343)
(878897799406381942654920, -65835263323776682753870819537864305)
(171678519786741026771736, 828969649803071576322242818239566127)
(-926435543649860084654790, 1411942050492430345345616669146658295)
(730095278106518984227410, -6922536030675705018220257258231705)
(656475990354078768559710, 187145049350138829148486966541955795)
(4492172729801233575685305210/6241, 29465418764959101182314345949378316202905/493039)
(642679416271510419949508250/49, 16205217604213064458716367249328689338585/343)
(11918775850464584385001170, -40881474318568931666227914658549489305)
(1660017688882463638399410, 1549639292643550966001498705096624295)
(595159272955029080711250, 283813970962553908228097219434837095)
(915952920458037019029210, -150966640729861185192288187963221705)
(-888194841551558286502590, 1419392828146056393405516186666098295)
(598205776390771152976110, -279213152813166576148786460663394705)
(-753499215156210324844590, -1424485874067932467154129398014075705)
(707765687557622168575410, -90872193136067515674820972136175705)
(870055765561001044171170, 31806765412019202650268909070818135)
(729843766909263041741730, 11329458880061171473385571859070295)
(716185911001982031139410, 70068842245628005449749220201224295)
(-695096082762136128287190, -1417422609583144936174281847878888705)
(1720926211449162851919810, -1675340898145515268067694925890066105)
(-1520847228835987906324590, -641361313063563030427352837136999705)
(661208573947140844530930, 179185082045237769237039959387804775)
(464263254054598951624410, 470011987575359054324909069711501295)
(-991314855910416496072590, -1392485774698853377716698751679431705)

Commentary

T=1595/2367

last edited by 7fff-zip at 2026-10-03 04:59:32 UTC · history