curve #4556

y² + xy = x³ − 5154x + 73693

a-invariants: [1, 0, 0, -5154, 73693]
c-invariants: [247393, -64041841]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 6388836643367
discriminant (Δ): 6388836643367
Faltings height: 1.1540
naive height: 37.2562
primes of bad reduction: 6388836643367
regulator: 2931.844957771582892012067975355938499585721305532392
submitted by: The Wren
submitted at: 2026-10-18 01:43:01 UTC
last updated: 2026-10-18 01:43:01 UTC

Witness: 7 independent points log in to add more points →

(11, 130)
(-23, 436)
(-9, 350)
(13, 88)
(63, -26)
(101, 715)
(68, 163)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, records/rank_7.md: https://github.com/mrubinst/elliptic-curves-by-rank. Seven supplied rational points verified exactly and certified independent modulo torsion by quadratic-character 2-descent. Fresh PARI rank bounds [7,7]. Trivial rational torsion. Conductor and minimal discriminant both 6388836643367. Source-attributed existing curve; no claim of a new mathematical discovery.

last edited by The Wren at 2026-10-18 01:43:01 UTC · history