curve #1996

y² + xy + y = x³ − x² − 5598400084645693858704704013720046724768623037762x + 4465124427198364141379890702453849205478114071956560532454248715182468161

a-invariants: [1, -1, 1, -5598400084645693858704704013720046724768623037762, 4465124427198364141379890702453849205478114071956560532454248715182468161]
rank (lower bound): ≥ 19
torsion subgroup: ℤ/2ℤ
conductor (N): 793627946783274194398421134715935644462180937975502965229114197476637198622092806630
discriminant (Δ): 2616864252663509739632544761060866413367405405082901632803598467802487003140602619998242572062703912310217510227421918047825686889407691739840416000
Faltings height: 27.0142
naive height: 348.3533
primes of bad reduction: 2, 3, 5, 11, 13, 19, 41, 43, 47, 53, 59, 61, 97, 239, 283, 331, 347, 373, 383, 1597, 4003, 4357, 4703, 88259, 1338923, 210728940797, 1296544412161
regulator: 163660688630699075604886541.5982324185559136489575254436212857951382034621552
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:55:12 UTC
last updated: 2026-09-26 04:55:12 UTC

Witness: 19 independent points log in to add more points →

(-2277264825279204175570279, -2324740085211369831543402585328211601)
(213995020095619043448853541/121, 411760523965680963083990279992243086849/1331)
(716829621650349619632161, 905739763510270588562591206073599599)
(186336511761954340458879461/25, -2426442089466230822345849686730596502949/125)
(6066391681493284427076641, -13919517677240421659717861650804466961)
(46615825657093044047907989/49, 4071642319898519581876234547590689057/343)
(2182511377572700392271841, -1625617120456335179028233547500354481)
(31820806771944663580101779, -179016520877361484048431529325371455609)
(2013119845670315259265901, -1163334561193803789686949421398771621)
(3051777493702810881853695, -3975212241950027551334901284594255553)
(949360226170353510728091, 76616155452825556744807175216070519)
(927645988177704344545301, 264680073617160262452123171191954919)
(10057691593228055954618291, -31073552460943609957755632992685752761)
(1750985257234199740903871/25, 252282064561523184998146147993594364691/125)
(1749572338082619820736201, -160515786875468847143003709751302321)
(-11556196619975021494143779/9, -83379786224692831106463364127854397027/27)
(-9306578279449865714479045/4, -17701244803342679773902676722885712839/8)
(1712682053834160057433299561/961, 11472259117439021480863534861540092234329/29791)
(-7553549306439313861525441/4, -23052039002316843390671081517197402793/8)

Commentary

2-isogenous partner of curve#1951 (Elkies - Klagsbrun (2020)).

last edited by Steps Unbounded at 2026-09-26 21:35:30 UTC · history