curve #3883

y² + xy + y = x³ − x² − 13718358505239354724793310777732x + 19283941770922557456727896714777815548166956839

a-invariants: [1, -1, 1, -13718358505239354724793310777732, 19283941770922557456727896714777815548166956839]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 129745795028517269811716096709715633845243163268310375483485634536394170 ★ record for rank ≥ 22
discriminant (Δ): 4581037622086986210684304929787140604986899406331052235330794936459386083893113436418457600000
Faltings height: 16.7717
naive height: 226.7025
primes of bad reduction: 2, 5, 11, 13, 61, 67, 79, 83, 45557928803, 4436386746053277759511, 16751513899225090331771500177
regulator: 238521942983171001248.2287252812052427618678625802900897433966173664538793169536231
submitted by: 7fff-zip
submitted at: 2026-10-04 14:05:26 UTC
last updated: 2026-10-04 14:05:26 UTC

(176550167398112173/9, -72944771671394456733689873/27)
(1914201077282997, -6180227081667588425299)
(13805330243857705669/7225, 4237412720372632001751936777/614125)
(583107525714604877/361, 251039947684778834642646559/6859)
(19304445132015117, -2635997750266501253142619)
(2402725807660494423/529, 2738960483602358098371210187/12167)
(2346716361335277, -3794037562982467791099)
(840156654317197, -91386034660226494721499)
(-407391151934448707/7569, 93177960147738606637010610403/658503)
(2412221503214597, -15115795125255240005699)
(5875242233951675653/25281, 510172813443991029534705633827/4019679)
(5192910295918660923/2209, 528877636778061894133275073/103823)
(168854389608615621577/249001, -12605857484880668237758806791021/124251499)
(67937211060886917, 17681885973288964549901501)
(26251444563394387/49, 37711577293979162471341809/343)
(851087205028645477/729, -1372089286563188559484392721/19683)
(1002536588134669386268037/67092481, 975471450207139770559575804281608771/549554511871)
(15023748699596997, -1790038704488129344439299)
(429048776399426563/9, -280210327341565737436252873/27)
(199347032139455617/81, -15090321965673198177623071/729)
(23237308877129695413/5329, -80081845342558300424564466283/389017)
(-1908854572485411203/1369, 9570758339023377276638550889/50653)

X1008, t=105/43.

last edited by 7fff-zip at 2026-10-04 14:05:26 UTC · history