curve #4665

y² = x³ − x² − 278014x + 8227528

a-invariants: [0, -1, 0, -278014, 8227528]
c-invariants: [13344688, -7028516096]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 1120143899616
discriminant (Δ): 1346661639284146752
Faltings height: 2.1686
naive height: 49.2199
primes of bad reduction: 2, 3, 7, 47, 59, 79, 1087
regulator: 1950.6144007595495095992791770063584825339435579866
submitted by: The Wren
submitted at: 2026-10-20 18:15:41 UTC
last updated: 2026-10-20 18:15:41 UTC

Witness: 6 independent points log in to add more points →

(12, 2212)
(723, 13588)
(1434, 50560)
(-198, 7448)
(2813/4, 101199/8)
(26, 1008)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six 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 18:15:41 UTC · history