curve #1847

y² + xy = x³ − 694084002440039602669221253644137468860x + 7051634654386386659409872390056330859308686612748964291600

a-invariants: [1, 0, 0, -694084002440039602669221253644137468860, 7051634654386386659409872390056330859308686612748964291600]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 40869197833097663292899752957410025726504827504743021536832255823772628910
discriminant (Δ): -81324593804439843832171963427521624142579002381875024782489336062484014516498126540327908565853941262079901900800000
Faltings height: 21.1243
naive height: 279.9244
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 157, 881, 931751, 81532414839977398595682093639673194422466631597
regulator: 18203830007044710742.211240645284270769071784543654402386474350675801621523848027
submitted by: Ritik Jain
submitted at: 2026-09-25 17:09:55 UTC
last updated: 2026-09-25 17:09:55 UTC

(1886651600488549420617382577959173290192/55769296978626065641, 62175383404846591811233203254682153584823759186944009103716/416478661288339116653643996811)
(-360406182792218412523180/11881, -17978176837721757023908857463991740/1295029)
(645975012467889286520, -16404680577271142059383913105660)
(12724676717661105080, -16732801549049134316340318460)
(47758796294036960834045240/1819801, -204090697179029912183675424685158172940/2454911549)
(384017769291615168256/25, 474223001186632631837033806964/125)
(239956902966675380525/16, 251368896604150346200927540715/64)
(-11540864536862017905652/1369, 5618546665088623543904328378382628/50653)
(82828789525902715555/4, -315782046619695312424637014405/8)
(11037339643797333932, 27118151316161969139897088736)
(624844316849166811280, -15605498596608194020783007262460)
(19275485257635662120, 28888163487255394338656512340)
(-27924709248324178330, 68252008926575689124933339840)
(115399763132730225305/64, -39012852540456903856981446484895/512)
(724016904334347639080, 19468809163107922964214848051540)
(1768419662943622601300/121, 7208684632677743972349801738460/1331)
(-16900934578322657980, -118129984129606467667964506360)
(-1674771915286927894630/121, 157524827406766818393461358650290/1331)
(14974111388254209620, 3987332267889941547360974840)
(4056496026403045640, 65596005575307449256099319940)
(13275196347212086572776602190236610/682713614606521, 537341750831161428380844666737199434916742955663750/17838479983481105233069)

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