curve #4659

y² = x³ − x² − 4304735x + 5205748791

a-invariants: [0, -1, 0, -4304735, 5205748791]
c-invariants: [206627296, -4496527191680]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 148576007943552
discriminant (Δ): -6595392104363786105088
Faltings height: 2.8859
naive height: 58.2687
primes of bad reduction: 2, 3, 7, 31, 113, 233, 241, 281
regulator: 7072.490325391586473653063237637905517291064524523053
submitted by: The Wren
submitted at: 2026-10-20 18:04:21 UTC
last updated: 2026-10-20 18:04:21 UTC

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

(-2242, 59853)
(-2290, 55221)
(3302, 164265)
(1671, 51726)
(67871/25, 14535006/125)
(7319/49, 23177442/343)
(-1961, 78118)

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 18:04:21 UTC · history