curve #3727

y² = x³ + x² − 187007333260373855236505x + 33354634447365659468049911685579819

a-invariants: [0, 1, 0, -187007333260373855236505, 33354634447365659468049911685579819]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 7883488166641953679773600245415288194780881496974344 ★ record for rank ≥ 18
discriminant (Δ): -62055438307538991562340341397288666250361781175713556607637273526160128
Faltings height: 12.3285
naive height: 172.5082
primes of bad reduction: 2, 3, 7, 19, 23, 31, 103, 118600364187985331, 283558558699368042216946123
regulator: 11971744969557762.661747125308643884733521789264340619559793845536827272253
submitted by: Matej Jurasić
submitted at: 2026-09-30 20:10:48 UTC
last updated: 2026-09-30 20:10:48 UTC

(593375371951, 362371623822366354)
(441546366973, 192009155864711850)
(7305410173, 178854295601490390)
(-148545672011, -240532706448297858)
(165019832731, 83597013261896946)
(230260815895, 50026110682500162)
(-173430318875, -246111612202091538)
(1151392070659, -1159500151976840478)
(143634351229, 97248408160813098)
(-6442826137109/25, -31729469405732841114/125)
(-350122349705, -236453171144593662)
(-321816462179, 245372129856936054)
(110316520165, -118605054578259438)
(-503270805389, 882828410369346)
(262723840531, -48554626701799554)
(194074261015, -66114267092330562)
(15567438672479581/2209, -1938774586497241502327094/103823)
(177427231403380537/262144, -62499778773221364136084845/134217728)

Specialization at T = -8/9 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-30 20:10:48 UTC · history