curve #2024

y² + xy + y = x³ + x² − 221524013053903269535173188x + 446695004412134084758084598242369075781

a-invariants: [1, 1, 1, -221524013053903269535173188, 446695004412134084758084598242369075781]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4730660125828472197497334873350
discriminant (Δ): 609532945889136719417654814256009953006813225037377137446208998753956417600000000
Faltings height: 14.1937
naive height: 193.6013
primes of bad reduction: 2, 3, 5, 19, 23, 31, 41, 47, 61, 109, 157, 193, 233, 593, 5749, 7549
regulator: 49431055488.25180656965266946267270411762608804151420626720
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:02:14 UTC
last updated: 2026-09-26 05:02:14 UTC

(104130586646589, -1051896371956355967887)
(-38844272060825/9, -981849967301117961151/27)
(438832414075, -18696727062693087913)
(289082046837925/9, -4392795167329977078901/27)
(-3183362780675, -33460822446657247663)
(18572307408144021/169, -2508148298955204134443739/2197)
(2231625855980325, -105419858990354467151663)
(-15500402213542575/1369, -1963990567262338248131939/50653)
(-15794612465675, -2302685958397486663)
(1901734330575, -5682692539469766413)

2-isogenous partner of curve#1933 (Elkies (2005)).

last edited by Steps Unbounded at 2026-09-26 21:42:30 UTC · history