curve #1942

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y² + xy = x³ − 82613215694870844749265589219800x + 292242952896116045212693917732319203249107850816

a-invariants

[1, 0, 0, -82613215694870844749265589219800, 292242952896116045212693917732319203249107850816]

rank (lower bound)

≥ 22

torsion subgroup

trivial

conductor (N)

4884689726378638346351305505912490586515437379287478166443278788626986587337135382

discriminant (Δ)

-810214202752213572573548628702643436130090031033293436192738405419771024708697630330449235550208

Faltings height

17.2119

naive height

232.1110

primes of bad reduction

2, 3, 29, 41, 179, 196039, 906869, 93312305791470539453, 230581728594610677347035765916523546849271969

regulator

43311033830130143976175.39116640550890935626513137831057601338752139217480232142653

submitted by

Ritik Jain

submitted at

2026-09-25 20:01:05 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:04:34 UTC

Witness: 22 independent points log in to add more points →

(2586886778816496, -309585725028046047436632)
(23962753181820852, 3474527321281352586797844)
(3986358487918134200162282304/52320615169, 249975563019620163406090645532794485988248/11967660551911553)
(221611687540702572484/45369, 700401325774453452508070180696/9663597)
(11571772832932142247/1444, 20883072894947419958356476903/54872)
(4531982459541292047702297706500373975209628/19062211753025821680043041, 9640941577096961368699602313720906301737263809744723601733136788/83226174828184188862823937125910904911)
(64547682465768579084/12769, -88987197760425748013012835588/1442897)
(112591908170327480712/1681, -1184240163191991269027488676976/68921)
(735719264788845304944/5041, 19917959748755021195439778942680/357911)
(4832880031196466, -76573258473201566951484)
(579484843681206852, 441072539112367346855890104)
(347965381675311696/49, 86563655768327997599821368/343)
(69849936687556080, -18311758824958729084744344)
(426423934923004304100/10609, 8597894506018167354818992203708/1092727)
(18523888920560705335264/2134521, 1491951585236933532386363574358280/3118535181)
(37964320646923904340/6241, -59974261127604773384486570424/493039)
(6843022425585198, 217616114338070339968254)
(14194152253417336737613573753601922739014543072/5002893777632949760588724618761, 3178683251537040449118710519202608452196134511980713587421016972778184/11190047316966019546888508530728842302174528741)
(79142966692934923177915672826036670852774617309823229521016582552437445026537236353069087517335206/16596657399336570106222364712381501078344995416075146855005669894417303157284923169, 175393739536563819471748673810556265949519932060821413530456884578615689248146862160557592457202063247656682349351773858640377339559237592000506580/2138114425202863853221144092536876297318845036197475584257007111571444223030689445216412336528970488408569178017741232405553)
(-137500320214260691267593214228479612563114415305195510510900906681502147437629980160719729081431554344083285076/13099177222506648550099973689645186972655062260449734671943847101025318284713250176647079944641, 79809315780152294105553359524555262865952380508659821707342184984509136449191027774742581060645747678311489377868291700919599295187485726828557892821081313203658140/1499222277071408468811086470101734510653940204576391468239276135634687232575142414072372513092466902325473142521884165446949103297098846566561)
(251853626653973717833130630382833936/36290915795458805209, 50403762734006530777735665696074484778647495822497240/218623524556564068065364003427)
(-7010896290889520503064167986/848895036025, 501547493323500124040289276434117524825578/782133685916813875)

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