curve #4688

y² + xy + y = x³ + x² − 20942335x + 36854030276

a-invariants: [1, 1, 1, -20942335, 36854030276]
c-invariants: [1005232081, -31849421399225]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 906500091605901
discriminant (Δ): 806057161955692351497
Faltings height: 2.9420
naive height: 62.1855
primes of bad reduction: 3, 13, 43, 61, 97, 109, 113, 7417
regulator: 9076.390330985304963833611985018380107365545230585647
submitted by: The Wren
submitted at: 2026-10-20 20:40:36 UTC
last updated: 2026-10-20 20:40:36 UTC

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

(-2274, 270811)
(3037, 34189)
(2402, 19203)
(9478, 825867)
(-4237/4, 1928397/8)
(49229/16, 2427459/64)
(-4308, 219283)

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 20:40:37 UTC · history