curve #2088

y² = x³ + x² − 269257607486550496912801x + 244606661587787782508468666572898975

a-invariants: [0, 1, 0, -269257607486550496912801, 244606661587787782508468666572898975]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 23354778245864734004307533064634560
discriminant (Δ): -24598255536124824273004055070438774374285693390493646779945076555540561920
Faltings height: 12.7644
naive height: 176.4931
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 29, 31, 41, 43, 53, 61, 71, 97, 101, 103, 113, 139, 181, 373
regulator: 134626083002.675186460383627562439976572126426296192064131948
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:54:12 UTC
last updated: 2026-09-26 06:54:12 UTC

(1294048017221, 1436361997109665284)
(1947606677969, 2666046777744676824)
(446549972450, -461968419064886595)
(-722563168126, 248824927915318701)
(430850618321, 456701901566389416)
(-464945328175, 518929246950903720)
(-241439232379, 543637579564379484)
(-274556166751/16, 31950169509492655911/64)
(-234588358399, 543011570820680976)
(-284900638486771/484, 4751707684103730800253/10648)
(-2686086920805766/6889, -308083927350881577391893/571787)

2-isogenous partner of curve#1202 (NDElkies); 4-isogenous partner of curve#1375 (jesper-petersen). Isogenous to curve#2087 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:40:04 UTC · history