An elliptic curve of rank ≥ 30
A new record has been set for an elliptic curve of rank 30, a significant achievement in the field of number theory. The article provides the mathematical parameters and coordinates associated with this specific curve.
Why it matters
Advancements in finding high-rank elliptic curves contribute to fundamental mathematical research and have implications for cryptographic security.
curve #273 — Elliptic Curve Rank Leaderboard
y 2 + xy = x 3 201769035260418549083594900060734240952308696994802735114305555x + 1151107939141058565733479426024323225135665982951300586808823640527729578307228357301072889377
[1, 0, 0, -201769035260418549083594900060734240952308696994802735114305555, 1151107939141058565733479426024323225135665982951300586808823640527729578307228357301072889377]
naive height 442.0854 ★ record for rank 30
Faltings height 34.7705 ★ record for rank 30
-46714661255308767314567688733841531918983356002159772613256840842851650254036518701100578342601553513579222272710220496887616034526983492843954090554197033638137245037791044053017600000000
2, 3, 5, 7, 13, 31, 41, 47, 53, 67, 379, 4349, 25721454817, 97018222656318846556561979214040553412450110580812087282349817173780902099339117104673990259247421230916714670243202937
10720686604115654188358042985326663938.588084900092986474567459949780498792191278825612795832355129
(-4761204159891138283979053265906, 44764265461782973805868732003346421827415264953)
(-14158422539541566469588779426546, 34199834254251713784176619895082644508395077433)
(-11522667358396562420423130332066, -44115070023357103726405378140637465204943359607)
(-204839531927226269712122049566, -34531574232452693997231136031282772551453427107)
(3899324051227528532535432912094, 20582352852872417675268569815574934013539218953)
(149851368287976334870008075289384, -1826442728148288630645637436047625928557963231657)
(240440240734591134232325971191694, 3721941824016160691689265341458606456425791434553)
(58446054919170749975942104376446/9, -289145377197241504032247540119122580900747897469/27)
(25642661602146479458845459929344, -113306861325798987289137854129016658652160209297)
(25720885078613923889202869994094, -113918565504468051036791617945007239588074855047)
(4956414590296956229584100339596814, 348939117745197814060339374812186839746231405619513)
(725964821994104294477684670330094, -19556488133953913131900670560396205869420775943047)
(20802191136944676997135829374, 33866070189878993817062821320678356972094522793)
(79052318332408565020526148386446/9, -202982221452031541387733280916787231176177841869/27)
(-11232245340662775388535509780886, -44725045659073489550941507272219743508825024527)
(8362456338772815315335239525614, -6972475614865802969141741730862843401376795527)
(2011658715643038193607509024534, 27447371869432010931671648582500375378543228993)
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