curve #2041

y² + xy + y = x³ + x² − 2797287263082156878497567441576187460x − 269518585763691523696475129027888915944168072727407035

a-invariants: [1, 1, 1, -2797287263082156878497567441576187460, -269518585763691523696475129027888915944168072727407035]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 181623693748207975822425210
discriminant (Δ): 1369467930454551523710563704111640872696513720151282236147043708205063813895206842858931244184845776129600000000
Faltings height: 20.0151
naive height: 263.3787
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 31, 37, 43, 47, 61, 101, 263, 463, 66943
regulator: 85950324.135329801635385908890467509170091962630994
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:07:02 UTC
last updated: 2026-09-26 05:07:02 UTC

(16230425471280569112853/5041, -1757066400926636262488311297898297/357911)
(16255468419926998418893/1681, -2040974784643101097961112955371767/68921)
(2496351640437995573, -2881694260685128046228186247)
(18044623255842481687/4, -71067688273132829266948971041/8)
(1691815447835982085093/81, 69362726961324189534612457327217/729)
(11454715339544803889981363/4044121, -31001715760918217183711320130982235737/8132727331)

2-isogenous partner of curve#1904 (Elkies (2006)).

last edited by Steps Unbounded at 2026-09-26 21:50:03 UTC · history