curve #2019

y² = x³ + x² − 1252663771253512060x + 220427527705627960960947684

a-invariants: [0, 1, 0, -1252663771253512060, 220427527705627960960947684]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 535701165729047061464726179383779596
discriminant (Δ): 104810692041541723575372531490209884617686715265786400512
Faltings height: 9.4430
naive height: 136.6290
primes of bad reduction: 2, 13, 17, 23, 29, 31, 37, 41, 43, 47, 53, 59, 3057053387069549573
regulator: 34333177779527.5854695518439311944081044139874861260901567372
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:02:03 UTC
last updated: 2026-09-26 05:02:03 UTC

(-2942430646616/3721, -6075796312478044858/226981)
(-2490017361968/2401, -2365107608361635866/117649)
(137819610174016/47089, -1502659004477541386246/10218313)
(659804098693694209/163216, -535947805421082146078614057/65939264)
(-1575630442307/195364, -1311083658678855119603/86350888)
(-46242064003259/40804, -111977535528450270881/8242408)
(-2044112015216/5041, -9206763521054791882/357911)
(133937543334328/85849, -1142659433587233200698/25153757)
(-21373482915872/18769, -33544344313056723782/2571353)
(74070152069704/17161, -616576352734249374502/2248091)
(10295515655443580503768/549574249, -1044653236749635584067549582334838/12883669119307)

2-isogenous partner of curve#33 (David Renshaw).

last edited by Steps Unbounded at 2026-09-26 21:39:24 UTC · history