curve #4380

y² + y = x³ + x² − 752472540665440x + 7944820409882916983056

a-invariants: [0, 1, 1, -752472540665440, 7944820409882916983056]
c-invariants: [36118681951941136, -6864325050850931985007384]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 145226302861035
discriminant (Δ): -45770648503124590037815102255469896875 ☆ record for ℤ/5ℤ torsion, rank ≥ 5
Faltings height: 6.9525
naive height: 114.3768
primes of bad reduction: 3, 5, 11, 19, 239, 599, 323581
regulator: 3899.81486607024018886086892738046135979191856832
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:09:20 UTC
last updated: 2026-10-17 10:09:20 UTC

(15805910, 217203772)
(16013909, 1218718957)
(-872203645/49, 42976497342316/343)
(87542405/4, 354108428771/8)
(-117710795/4, 542838746171/8)

Curve from torsion/torsion_Z5.tsv.gz:1289 (mrubinst/elliptic-curves-by-rank) + Werr 4-Pillar Algebraic Sieve factorization.

last edited by Volkan Dagli at 2026-10-17 10:09:20 UTC · history