curve #31

y² + xy = x³ − 2060795223235870670x + 1037860392073475481628988676

a-invariants: [1, 0, 0, -2060795223235870670, 1037860392073475481628988676]
c-invariants: [98918170715321792161, -896711378899860072200428904305]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 240767746179482941231124244768162
discriminant (Δ): 94793787423403087849353656317664770631480997068191076352
Faltings height: 9.4779
naive height: 138.1225
primes of bad reduction: 2, 3, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 697675341112349
regulator: 17736686.04120010720386049179366267873878228181167867826206
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:10 UTC
last updated: 2026-07-01 22:51:29 UTC

(150913924, 27023891033530)
(1309368796, 24172933593538)
(1714332274, 50430125403496)
(1088122156, 9154278492706)
(1080521116, 8523778305538)
(1048497604, 5456990794690)
(153591884988, 60191191934061474)
(1028141818, 2427298113664)
(1023547336, 925461825238)
(-1104208292, -44351144023742)

Found by Kretschmer (1986). A curve of rank exactly 10, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:03 UTC · history