curve #690

y² + y = x³ + x² − 716978538337448692531833726491639679916937440x + 7080033660194149939592921884186148542059385683057762819054175316806

a-invariants: [0, 1, 1, -716978538337448692531833726491639679916937440, 7080033660194149939592921884186148542059385683057762819054175316806]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 264134895515802938818712517932592996942874287806233003404355064648131144811687859335597946410983285905
naive height: 321.4645
Faltings height: 24.7196
discriminant (Δ): 1933587016180761820239780743436730109234775959976493880177104394726847107741213403484087978484278621290778341946941051835865667334453125
primes of bad reduction: 3, 5, 7, 11, 13, 17, 23, 29, 47, 67, 71, 131, 4815381486563553742270608461334883574480323928029721748020913460312371378956121844687
regulator: 2435948701161076929693735092.44712853592013510606329877719512526970339028854254142155527371
submitted by: FNacc
submitted at: 2026-09-10 02:04:56 UTC
last updated: 2026-09-10 02:04:56 UTC

Witness: 26 independent points log in to add more points →

(-13367667281833233649000, -3778311157919584421168912756824958)
(-9987716820911418243802, -3639325857499535612668722381826562)
(-24513270637426642230625, 3150474180965761528331662253945917)
(12769341598760126880815, -82514438686119065305125422919443)
(-27726221035308215966140, -2375877001096583659143843468942803)
(-8893301531572777050505, -3571128890509724335521077224653563)
(29311380782266968979370, -3353726578010346672021408531650063)
(-10765927961515897085755, -3681188105471584495693220810576813)
(1742724191433592616799865/144, -723966479148799237608830943728964469/1728)
(12764927889841257510695, 88401736741070007210852872713237)
(9451378326235903620815, 1071389838188139343996926790820557)
(-16710121562168788132452815/576, 25729756620569217712881667789671092023/13824)
(-29526674196239037696025, -1583650126035308106896532110710358)
(-29130849600384902758255, -1801555512416722338335823144295688)
(-74153285787791061823615/16, -205432828375618041316310318417780297/64)
(-30755721821736733512130, 197345437939978007880129863367937)
(12796833481675162149545, -23972339618484783699097967054513)
(21403732639920258456143, -1240761786531645558063216341890382)
(134014651297493909878250, -48144446483963126206242116707881458)
(119148564976479579451966370, 1300568446218462610402010305181993882062)
(18003538444819533781490, 85574678767849852524682716459982)
(3641025861464960790802295, -6947426055599970068584283105194053638)
(18553973034944313221570, -405508126326034940753353579533263)
(64892753563079093494850, -15291213656574201179332368070536143)
(643655208685760002800845, -515952337516398548941629915569744213)
(426059636329632714264170, -277565942888240344052321365692170738)

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