curve #1702

y² + xy + y = x³ + x² − 6463754804116253375x + 6325444251979261499767199685

a-invariants: [1, 1, 1, -6463754804116253375, 6325444251979261499767199685]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 67253165913064670
discriminant (Δ): -1242409264384460313599349640149718552852879882812500000
Faltings height: 9.4606
naive height: 141.5519
primes of bad reduction: 2, 5, 7, 11, 19, 31, 79, 11491, 163351
regulator: 35573.524382348840269388155897457215765460929466834
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:12:38 UTC
last updated: 2026-09-25 06:12:38 UTC

(-11834855547/16, 6620806967445437/64)
(1161185583, 19633884454958)
(1538331583, -4739175795042)
(1975719137377/1369, 86096762942566324/50653)
(42780209547/484, 807761810713939659/10648)
(101254086853/16, -29941113162683313/64)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:12:38 UTC · history