curve #4660

y² + xy = x³ + x² − 5936153x + 5502099057

a-invariants: [1, 1, 0, -5936153, 5502099057]
c-invariants: [284935369, -4755950600453]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 282469347104010
discriminant (Δ): 297635126350024296900
Faltings height: 2.7370
naive height: 58.4033
primes of bad reduction: 2, 3, 5, 11, 31, 103, 3001, 89329
regulator: 2672.013156547243211885681376482495094541852227226093
submitted by: The Wren
submitted at: 2026-10-20 18:06:01 UTC
last updated: 2026-10-20 18:06:01 UTC

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

(-1873, 101207)
(-1667, 104606)
(-19, 74942)
(4616, 274247)
(2041, 42497)
(6641, 505622)
(908, 28901)

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 18:06:01 UTC · history