curve #2099

y² + xy = x³ + 556343713390195470809443812379910x − 2765121350121174071438566538948343580219171150300

a-invariants: [1, 0, 0, 556343713390195470809443812379910, -2765121350121174071438566538948343580219171150300]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/4ℤ
conductor (N): 59581557002530875732300241072530
discriminant (Δ): -14323735948166665003296584008825264146272511801982320304880182200168979823748935162217549448459521600
Faltings height: 17.9063
naive height: 237.8104
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 31, 107, 163, 563, 887, 1621, 1823, 6701, 9341
regulator: 203367184191.95135492731657200855887559120525415013388617
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:56:22 UTC
last updated: 2026-09-26 06:56:22 UTC

(15193542768034880, -3032333254032873894679750)
(60976619909430385088/529, -485596629112692611506978722026/12167)
(2250058679645410522269230/41460721, -3653257188706751754061637341991424250/266965582519)
(13429627009968162976/25, -49261803340038471422301125266/125)
(59394945099276182, -15485798846281145844884854)
(2826544392721270048/49, 5102214485520639171543412618/343)
(87123480036454130, -26589778562340415150337500)
(37922934069414383/4, 14667720848175459110035933/8)
(478121037142276002703877/309136, 330641311177186385009227829711590577/171879616)

2-isogenous partner of curve#1827 (Klagsbrun (2020)). Isogenous to curve#2033, curve#2098 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:44:57 UTC · history