curve #4672

y² + xy = x³ + x² + 42500542x + 1215661881042

a-invariants: [1, 1, 0, 42500542, 1215661881042]
c-invariants: [-2040025991, -1050316565025293]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 131859174638950710
discriminant (Δ): -643318793555035655469446790
Faltings height: 3.8236
naive height: 69.1757
primes of bad reduction: 2, 3, 5, 7, 41, 43, 73, 10369, 470521
regulator: 4584366.40874571041846578176073116608525390236799897864
submitted by: The Wren
submitted at: 2026-10-20 20:20:02 UTC
last updated: 2026-10-20 20:20:02 UTC

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

(-9297, 135276)
(67099, 17464200)
(-8891, -363054)
(48969, 10963041)
(12699, -1956600)
(-8483, -490503)
(6147, -1310448)
(270979/25, -215369943/125)

Commentary

I obtained this curve as a rational 2-isogenous partner of curve #4650: https://elliptic-rank.icarm.cloud/curve/4650. The source curve appears in Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I transported eight supplied independent rational points through the isogeny and checked them exactly on this minimal model. Same rank and conductor; rational torsion Z/2Z. Source-attributed isogeny construction.

last edited by The Wren at 2026-10-20 20:20:02 UTC · history