curve #262

y² + xy + y = x³ − x² − 21065871080015087031831279377x + 1192838816489664881520195774886398643920001

a-invariants: [1, -1, 1, -21065871080015087031831279377, 1192838816489664881520195774886398643920001]
rank (lower bound): ≥ 20
conductor (N): 13935395240740481313503432825112888552210319085746508942961924055710
naive height: 207.2930
Faltings height: 15.1523
discriminant (Δ): -16378489773890508615877080165901846553233993421151363692197420638035049197392224000000
primes of bad reduction: 2, 3, 5, 13, 43, 67, 139, 2255302853, 10014475523365307, 1316868143848259879536307103829267
regulator: 28617395134410392694.9422195314721435929124050804019701278758727416220700100201
submitted by: David Renshaw
submitted at: 2026-07-29 16:41:18 UTC
last updated: 2026-07-29 16:42:50 UTC

(92331349006391, -186897008859628773356)
(88705028573201, -148905786054078962026)
(-157122187205489, 789822302208319400084)
(629803441742851, 15418771095396632764724)
(-357553570399, 1095614416018862363974)
(38967499350391, -656601361205992549036)
(85374389273551, -128952053792301087076)
(1663419347231851, 67592696901177875839424)
(-139318422848749, -1193140615464458778376)
(46220321389041199/49, 9825673404350102386257932/343)
(405200552356471, 7693230386475427074644)
(88348658380501, 145950411040012477874)
(70042111935001, -246901096645556298376)
(77046000402151, 164770719932806676324)
(-103260109262309, -1505681370473604416236)
(2649405440431/9, 29411880947588238525308/27)
(81200969682901, 132951704196597596024)
(56088792806634371/121, 12699080969194259046826544/1331)
(1094883105093751, 35925479444035541719124)
(-154281527774839, 877828541614530892984)

Mestre integer-(u,v) family wide-denominator sieve (M6000 native), fiber T=1459/4; famcert3+wdeep2 QB=1e7

last edited by David Renshaw at 2026-07-29 16:41:18 UTC · history