curve #4999

y² + y = x³ − 19623904

a-invariants: [0, 0, 1, 0, -19623904]
c-invariants: [0, 16955052840]
rank (lower bound): ≥ 6
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 228205984230675
discriminant (Δ): -166362162504162075
Faltings height: 1.9833
naive height: 47.1077
primes of bad reduction: 3, 5, 11, 52859
regulator: 11822.430520616502885792181471389957318247068504033
submitted by: The Wren
submitted at: 2026-10-21 01:44:20 UTC
last updated: 2026-10-21 01:44:20 UTC

Witness: 6 independent points log in to add more points →

(276, 1183)
(334, 4199)
(456, 8671)
(564, 12640)
(1626, 65416)
(7681/16, 610527/64)

Commentary

Rational 3-isogeny partner of Daniel Błażewicz's curve #4998: https://elliptic-rank.icarm.cloud/curve/4998. Points transported by the rational 3-isogeny and reduced with PARI/GP. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion trivial.

last edited by The Wren at 2026-10-21 01:44:21 UTC · history