curve #4289

y² + xy = x³ + x² + 11008249x + 381684854859

a-invariants: [1, 1, 0, 11008249, 381684854859]
c-invariants: [-528395927, -329771751628661]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 26676134520303198
discriminant (Δ): -63019061057257303010879118
Faltings height: 3.6296
naive height: 66.8588
primes of bad reduction: 2, 3, 7, 29, 73, 127, 457, 673, 7681
regulator: 5322380.50857306883571389494129465821736224988096328238
submitted by: The Wren
submitted at: 2026-10-16 18:49:14 UTC
last updated: 2026-10-16 18:49:14 UTC

Witness: 8 independent points log in to add more points →

(1807, 637439)
(-2459, 584114)
(6591, 857295)
(-26897/4, 512107/8)
(-4679, 479589)
(17431, 2414130)
(2757, 656649)
(-1199, -605011)

Commentary

Obtained by a rational 2-isogeny from curve#4045, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor. The eight supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:49:14 UTC · history