curve #4657

y² + xy + y = x³ + x² − 4316841x + 2291336934

a-invariants: [1, 1, 1, -4316841, 2291336934]
c-invariants: [207208369, -1981269173897]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 617897437263645
discriminant (Δ): 2876809977899264709225
Faltings height: 2.8210
naive height: 57.4477
primes of bad reduction: 3, 5, 7, 11, 29, 139, 10789, 12301
regulator: 3951.619600748757461383526534434440289158736267180731
submitted by: The Wren
submitted at: 2026-10-20 17:52:34 UTC
last updated: 2026-10-20 17:52:34 UTC

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

(-2302, 7197)
(-356, 61685)
(3324, 155445)
(12894, 1439420)
(-4249/4, 607155/8)
(189, -38595)
(-2163, -37839)

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 17:52:34 UTC · history