curve #1848

y² + xy + y = x³ − x² − 4407502257701732413617308203602x + 3415620428102910574889671021568349207408102225

a-invariants

[1, -1, 1, -4407502257701732413617308203602, 3415620428102910574889671021568349207408102225]

rank (lower bound)

≥ 22

torsion subgroup

trivial

conductor (N)

52278795386414421832423298705830573585936145109581634301451947152002746318

discriminant (Δ)

439798391153030676115743337252776790933325254160165183758880296124327141439246662755546857472

Faltings height

16.5378

naive height

223.2962

primes of bad reduction

2, 11, 13, 19, 29, 37, 71, 83, 8623, 39813737250543269700871, 4431782545651410291174406441535682671

regulator

972564692445450855025.7826239548113831273565164451233351035714825669968799466562647

submitted by

Ritik Jain

submitted at

2026-09-25 17:10:11 UTC

later contributions

(457054114999899126279995616960699249/146528472696074219776, 250941870394830508103696482757228497418939421093112945/1773711714368272919459934334976)
(7765435513146801, -661408085557629317449969)
(-290777889414411175/121, 15137989440003529958967325/1331)
(3449630370791053675/9, -6406964873541481264217187827/27)
(1877175007554017, 41913366526259122510255)
(14373957937273417/9, 572875976276937147221813/27)
(-224012745484945479/121, 96256084848836001580102461/1331)
(13524117359025213, -1554796707110164659680581)
(15937461278861197/9, -921058610532885532897331/27)
(1415583933522721, 3617784067460674538671)
(456799183782101509/16, -307923371159776321903335155/64)
(5036425695310338493/2601, 6138386988076130280929234269/132651)
(-178176883713761319/121, 109051343221212519932447197/1331)
(-17207604104174807/9, 1880966368550181676337525/27)
(8343923296644456865/289, -24040042480150704917939268385/4913)
(4738711209306267721/2025, 7009060307552560241920027259/91125)
(-77003010162264371/169, -160384866457063013811803841/2197)
(939298109024177, 10216980897420144853775)
(-216540741139179328919/145161, 4517192090472222318441604588811/55306341)
(30223694243097874045/51984, 383989509246097412965982057483/11852352)
(440850570342001, 39474669010129613612431)
(23674796061356844201/24025, 20146530963156145211985533709/3723875)

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