curve #4129

y² = x³ − 26469021249413257792824928681206891614676007x + 52651752481930128056902630908591626822058612743513500086941484106

a-invariants: [0, 0, 0, -26469021249413257792824928681206891614676007, 52651752481930128056902630908591626822058612743513500086941484106]
c-invariants: [1270513019971836374055596576697930797504448336, -45491114144387630641163873105023165574258641410395664075117442267584]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 35600437463689094599759825138642952742018081983479997265582344315740036858149485518643791681899972637662779941640
discriminant (Δ): -10749486963539118723022904728412301870333331291430508491167857060546866071344028510437419966004443711793436771189820423080851680000
Faltings height: 23.7961
naive height: 311.5763
primes of bad reduction: 2, 5, 7, 11, 47, 61, 107, 55829, 74586683, 1558136431, 30949955611, 82349340260085214078969, 227894828119014569698063, 9997971603001541437726813
regulator: 12020842530789212225016556810496.442460926915517553741038178080062881473814065243961721579151
submitted by: apkorte
submitted at: 2026-10-10 11:09:49 UTC
last updated: 2026-10-10 11:09:49 UTC

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

(2984427287391571374037, 15446642420904908154493980816850)
(-1441480683198746352583, 296329429533384728658354187147970)
(2903760547852155616617, 16614889288807501908376102866770)
(-414845082438076415353, -252112876349768925688311796238260)
(4618626026136693015437, 170071797403958424725875628199850)
(-4629016044054393584293, 275658656611021193165836813073980)
(-1421574322122297168935/4, -1992205368914028736715294799894373/8)
(968456764539788032501, -167110662849995420337707412743410)
(4714714224448707628295, -180718148226765791546297802674804)
(-5302353924628487222658, 209581530298028234334712327260580)
(4612844998459339456037, 169434175230398441480656231997150)
(15932177711496152805922, -1917048660299991333668818669159910)
(2832128284315876608901, 20110938764154477124169064653950)
(4807796111570511482107, 191117340841277777895097107937420)
(956901138695091894142, 167927698141787196478405288205380)
(2341019745137219411257, -59303571165960688785195074821570)
(32277407479231321033927, -5729389597803546639624964528823060)
(3094375078086289398085, 19385570904895308307426227728194)
(17249651915423189425001, -2174560357844106040648233566004910)
(2778920169550053067377, 23587732027504235696813527853110)
(-595190643379781663838, -261141760068265150988614022441350)
(194248679749306153599577/16, -78923488112984908341463334404211165/64)
(2523334642056975012027, 43910992447821084465923120460460)
(2935022630282152119907447/1521, 5552176309614767588687460726232619780/59319)
(2798106506808769628037, 22273460555088865453863443838850)
(-18254355839843700683255/9, -8452073895611849875274946186544478/27)
(7876700201489801232700777/576, 20726308002839610483316060654460685515/13824)

Commentary

Specialization at T = -1844/499 of the rank-17 fibration of X1008 given in curve#3594. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-10 11:09:49 UTC · history