curve #1683

y² = x³ − 41958111379778430395819744068558060628793836727x + 3291388265147587654133062055255469697492488762537470118848717304500154

a-invariants

[0, 0, 0, -41958111379778430395819744068558060628793836727, 3291388265147587654133062055255469697492488762537470118848717304500154]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

51002649503092728277632696145784189389596575181337812584075629264209254935749000427731071534072558069054792361960

discriminant (Δ)

47500712277498269566241811576643753596541590304663404384531646383001429381186238249141549741307316249761374172511699068242423161154964000000

Faltings height

25.6422

naive height

333.6726

primes of bad reduction

2, 3, 5, 7, 11, 17, 29, 31, 43, 47, 79, 527543619607, 129941068530393118193397484023819501128601666298837091883666319231415267784418076336297

regulator

825533081356083552390590139269.03610986639221998830964240476014455035047360756406733696733812

submitted by

Ritik Jain

submitted at

2026-09-25 04:08:51 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 05:05:23 UTC

Witness: 27 independent points log in to add more points →

(660078824718103306547196754535490825654058033712453586222/4615830698305223344499115094309249, -4605194997000260478508730404339601522424267268371668686891000036012415605202796457500/313599099373204065484763620179560995276941206933057)
(129129072962488743695133, -5149310481091758304344118129172910)
(39656898952989428382888451165/247009, -3232532992698764593042847459738169316745006/122763473)
(7183963354383048559762131/25, 15290405954181690602829965873077483404/125)
(548855271111470326361859633/5041, 1327498537258630932136717408959996546030/357911)
(-32490552793302217863315, -67973026269063178403193528406560222)
(-213254666404081283129057723/4489, -21641229471084437321840973222056512602010/300763)
(960797986393371937512801/4, 672741148857421111467180226135061895/8)
(-827886212201779660087265283/9409, -72452783316400426336448465587893557701710/912673)
(93508539159452797144953, 13622441557554304594662965287764150)
(-521526973480293144706861893/5329, 31267680279192006442053061900554417681180/389017)
(57591979925131519649032537/729, 426583440110422806573775104488196496250/19683)
(-231988746559187947689063/4, 594898691096786676751920219468615675/8)
(483894023038182009359865, -310312023678410497387033272173436618)
(1484005971691953037012101681/16900, -37030696834365164971670423406163898883921/2197000)
(106794055971208829296513, -5338016136396971934065357010613570)
(100775719849351711078210653327001933/54694709161, -31801602759478487842324953876323346430982924768525150/12791396936773909)
(476259568054424093868466979428937449/4821186318400, 111304260575453982617821235553469673005040456922674293/10585975223037248000)
(2706281206890449711982643789/25281, 20711506069334561007969470679962292642430/4019679)
(-3488115101931469261736963994667987845812430453/17433390545549731618849, 139570753993910121901978279856682793029106985742788063330499998202900/2301827578514376529209319714498993)
(287516265191568173245200979399707754756884765102/3710642925550072914820609, 160706330744791909169964907779782510991209675268445967134189586449716300/7147822289031733312550734472527518977)
(110016186378004098338103756381453782529344050243249/6765185585145139458274862721, 28445876234225746390956344233587642238040049983770397254283906308612132971950/556441576323854105044651304871975382700481)
(822517731310070381046417/4, 463606058073092781600118712115607905/8)
(222663978893281982616460025730/1142761, 61244517918766250459851567782268859691915258/1221611509)
(54494299175249260877730102314477158010733/602210891017395361, 7172611050967499223957845476969256314213422323670702783425250/467329189732539762201110641)
(52095481722101694545356406486595989293/62571406423681, 365557625592167937582324946198446840161539705944925387550/494952902235259259329)
(18772260985070110927935042/169, 2484650193757253149771390277437081290/2197)

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