curve #4023

y² + xy = x³ + 11846273771479827152700186296728304772410x + 9966409739975534371472949346296292161891501628610053499806436

a-invariants: [1, 0, 0, 11846273771479827152700186296728304772410, 9966409739975534371472949346296292161891501628610053499806436]
c-invariants: [-568621141031031703329608942242958629075679, -8610978015338861696951775303488449880319262993705721785889147185]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 100333804916069595557644850229910002358198035153406924766836550463004943183082
discriminant (Δ): -43016663573687271933898947634670450188852045984282007227924321986240777342507467612061512245823300597964579994697753108873088
Faltings height: 22.5942
naive height: 294.4318
primes of bad reduction: 2, 3, 11, 23, 73, 83, 89, 127, 157, 197, 199, 353, 541, 563, 757, 853, 4703, 6449, 25471, 29833, 190711, 203857, 304063, 437153, 18963911
regulator: 469480277139169630485089262.57452701837558326828543447518430548866081563024
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:47:58 UTC
last updated: 2026-10-05 04:47:58 UTC

Witness: 18 independent points log in to add more points →

(709957347969041571956, 19396475454182669928178486277786)
(911413394681994953636, 27889980552479929103724191842106)
(13085667497197703851946, 1496958666917335151005789925421608)
(84044732244206789212079716/3721, 770497044188261356042439650307366786698/226981)
(68101636646026679519/4, 25516153265702077696990725503689/8)
(141464585011100198306, 3804373744328455191324615495758)
(782614938522471112607/4, 35574262617501871275852547710289/8)
(750039709135591143728, 20995085095620287313352764143594)
(-5288866552998774961629596576/105206049, 3280855450590078302530888576151045271004438/1079098444593)
(-1112994392247678175817836588/6880129, 35256226267418412329366056344208535085998/18046578367)
(651583014426545916499892/529, 529407020132723487370313990916292918/12167)
(12948205047013709319523024/42025, 56404377153965886341904835761483780658/8615125)
(-802361720654205488598908/8649, 2284862836394006096742829461590016106/804357)
(-601746800477551743637381324/11122225, 112306274744830249697855212263679030185046/37092620375)
(248669433198046109929320418436/899940001, 158198257799821373574474383459951615303544742/26997300089999)
(3369064646260046695257463886584/2943388009, 6232239372088036952062026598158789963778540882/159687629652277)
(40153717531302495944949762694/176703849, 11600961264821800354917419613011412595380556/2348924264757)
(872283619367036423476942716349972/3295905904369, 33656859888544038077203375261954891322059791024286/5983595220863457847)

Commentary

Unlisted rational-isogeny neighbor of curve#3723 (source contributor: Matej Jurasić). Source equation and witness provenance are credited to that entry. Exact rank 18: 18 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:47:58 UTC · history