curve #4287

y² = x³ − x² + 232483235314x + 4369155892639560

a-invariants: [0, -1, 0, 232483235314, 4369155892639560]
c-invariants: [-11159195295056, -3775017646412350208]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 1739383412924152840357920
discriminant (Δ): -812429981788170592686048309915840960
Faltings height: 5.5799
naive height: 90.1299
primes of bad reduction: 2, 3, 5, 11, 23, 31, 43, 139, 331, 6121, 1230769
regulator: 3271578648.902436167598643564661241729670450238899062277604
submitted by: The Wren
submitted at: 2026-10-16 18:43:10 UTC
last updated: 2026-10-16 18:43:10 UTC

Witness: 10 independent points log in to add more points →

(-13724, 34292432)
(52524, 129325188)
(5093356, 11546501932)
(381924, 385836288)
(77956, 151546568)
(1357164, 1679177652)
(4098789/4, 9186179931/8)
(12662701/4, -45582550631/8)
(447724, 445203988)
(691884, 704576028)

Commentary

Obtained by a rational 2-isogeny from curve#4097, submitted by Michael Rubinstein and sourced from his elliptic-curves-by-rank repository. This isogenous curve has the same rank and conductor, with smaller absolute minimal discriminant, Faltings height and naive height. The ten supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:43:10 UTC · history