curve #4661

y² + xy + y = x³ − 6178344x + 5211423842

a-invariants: [1, 0, 1, -6178344, 5211423842]
c-invariants: [296560489, -4503115040437]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 890748021049810
discriminant (Δ): 3358734655492308068900
Faltings height: 2.8592
naive height: 58.5233
primes of bad reduction: 2, 5, 7, 11, 59, 83, 5009, 47161
regulator: 3660.686868383199393163899595337552481992216963675732
submitted by: The Wren
submitted at: 2026-10-20 18:07:35 UTC
last updated: 2026-10-20 18:07:35 UTC

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

(-2309, 85819)
(-1424, 106174)
(995, 6523)
(759, 30595)
(4039/4, 8937/8)
(701, 34649)
(2293, 54549)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Seven supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.

last edited by The Wren at 2026-10-20 18:07:36 UTC · history