curve #5849

y² + xy + y = x³ − x² − 110825482060110212455639655x + 457561442584719016299457644836026300447

a-invariants: [1, -1, 1, -110825482060110212455639655, 457561442584719016299457644836026300447]
c-invariants: [5319623138885290197870703425, -395333086393173291778606421332436305421025]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 4864621857441501576748303296835966654974471279574715826312503550
discriminant (Δ): -3328401129940280527359439133259741643450482889546066651179517951847997726720000
Faltings height: 13.8559
naive height: 191.5611
primes of bad reduction: 2, 3, 5, 11, 61, 127, 337852693222131285623, 375476660541025531712315031428748409
regulator: 2160246406249984060.66977813499212073884040309144911554478538202604783378136422
submitted by: apkorte
submitted at: 2026-10-25 11:49:01 UTC
last updated: 2026-10-25 11:49:01 UTC

Witness: 20 independent points log in to add more points →

(-5963104238141, 30106242094198670510)
(6132089929039, 2924325345667050590)
(8169139938055, -9868077731260806694)
(36000196473139, -207664618271600602210)
(6421558392499, 3269731781999444510)
(-3504248317661, -28335314310891145810)
(5423751432349, 4002809191765325690)
(13639698631105, -38516024340708080044)
(35133421299149, 199827602823074823290)
(1317318045029, -17715954275876357830)
(55456968270019, -406039501148211502450)
(-3565373031581, 28414311841064085230)
(-3362764692577, 28146310334675739230)
(7086586322065, -5298435084188261014)
(43128911099095, 275503145058819255326)
(3511660027939, 10568108875205369390)
(6220295012995, 2978308421533174478)
(4332779615059, -7662784601347971970)
(-10553635101661, -21253642862616024530)
(5855118083203, -3064754818736602450)

Commentary

Specialization at T = -5/2 of the rank-17 fibration of X1092 given in curve#1842. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-25 11:49:01 UTC · history