curve #1879

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y² + xy + y = x³ − 1855084544775656135718889337333422688x + 1050141173357237487435186085944596059435572114244703906

a-invariants

[1, 0, 1, -1855084544775656135718889337333422688, 1050141173357237487435186085944596059435572114244703906]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

69062427480259048824550406812767439577003784449886971318180672520277543824578700418867349370

discriminant (Δ)

-67833733761766766725202599004311914114706476619026417283566709466227560777849019459991558354240268275080762500

Faltings height

19.8161

naive height

262.3002

primes of bad reduction

2, 3, 5, 7, 17, 37, 137, 229, 2557, 13098079, 4436897895547531, 112149691048155118430344676160052103091968756852985002437

regulator

98117630437747006002790225.26591864505898819693294884112275301951427033426562120102189834

submitted by

Ritik Jain

submitted at

2026-09-25 17:33:45 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:41:47 UTC

Witness: 25 independent points log in to add more points →

(-1395228963685692959177300/2424249, -5239924568655084609327897735733825159/3774555693)
(148748086249305634062127229300154487920895/40430323972620831536676, 53940204668402465813311395316505712711364335575110592484629083/8129443781833569898069367234078424)
(47902123514974433025, -331404652891339939387316716463)
(24022989785696561967, -117559558875231133923796766561)
(3341440815943068390, 5670928516785324016730912287)
(-1469549778977042565, 776321461297575854238284287)
(-35955485312884470729/25, -107764120595637309371875734259/125)
(42146433170953992165/16, -243211013660107569273286353257/64)
(160038987206415364290/289, -2156535824521132437794672628094/4913)
(3087045727874936478660/2209, -113111295211687626488301163444294/103823)
(-1571499593449375785, -290539398397609922281101713)
(-556785679122889249569/676, -24975974752841077530428975463331/17576)
(-11011526561267745200/9, 32938984813657918408213736299/27)
(92980471499140850175/121, 372642878302669164498829073147/1331)
(250868871787299800, 774949473620442926990650137)
(-1400158489699461782427/4624, -395747561903787813389826579228169/314432)
(-1809742343044389177/4, 10723685323282898322047358737/8)
(-624121599610142175, 1401722801461851397600443937)
(-1575197001324197100, 252614663621269460091398437)
(213333319454443439351137358376421109795369715672/92298456962753262404380437241, 84636540473816142170718537032898660708529862010541358664409040842007498/28040881421844213579790567538900723523652211)
(544207098923814900, 449181603395199626648726662)
(-1563269472715143285, 360280979364340027368342037)
(-825189210895670025, 1420927467384134208919614937)
(-2253693515641971618263222409748200105/1703437527648854209, 2423900568933180015337177002790328120744071856682277351/2223255196772687061206169823)
(632736800202168883214940/14922769, 56821020222520649939970934165960865819/57646656647)

Commentary

Specialization at T = 134/19 of the rank-17 fibration of X1092 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 55383T^2 + 56058T + 719878, p = -114347T^2 + 352493T + 61050, q = 169706T^2 + 291795T - 41886, D = -28328439982T^4 + 102089108086T^3 + 44484660298T^2 - 200379282670T - 5489566500, E = 7(2524119806T^4 - 4100464067T^3 - 2893055278T^2 - 2444573283T + 1576980522).

last edited by wgxli at 2026-09-25 18:45:30 UTC · history