curve #4656

y² + xy + y = x³ − 2768377x + 585251016

a-invariants: [1, 0, 1, -2768377, 585251016]
c-invariants: [132882073, -505856201149]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 460062135545738
discriminant (Δ): 1209776631258259370372
Faltings height: 2.7375
naive height: 56.1149
primes of bad reduction: 2, 11, 17, 79, 89, 257, 7649
regulator: 6047.239806513689634045900511576783847218876415330994
submitted by: The Wren
submitted at: 2026-10-20 17:50:09 UTC
last updated: 2026-10-20 17:50:09 UTC

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

(-1743, 11640)
(-1523, 36390)
(-764, 47863)
(2173, 68422)
(-577, 44904)
(-1387, 42612)
(8937, 825990)

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 17:50:09 UTC · history