curve #4678

y² + xy + y = x³ − 46127331x + 120578612558

a-invariants: [1, 0, 1, -46127331, 120578612558]
c-invariants: [2214111865, -104183242418125]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 153306369327950
discriminant (Δ): 42502657832480858000
Faltings height: 2.9790
naive height: 64.5544
primes of bad reduction: 2, 5, 29, 109, 239, 349, 401
regulator: 7032.840127861517786234198663890684597249988619740674
submitted by: The Wren
submitted at: 2026-10-20 20:28:31 UTC
last updated: 2026-10-20 20:28:31 UTC

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

(-853, 399556)
(3931, -1104)
(103, 340284)
(4971, 116356)
(4883, 106064)
(302, 326461)
(6247, 272956)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. I checked the seven supplied rational points exactly on this minimal model. The source records rank 7 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 20:28:31 UTC · history