curve #1482

y² + xy = x³ − 10596063090767790103x + 20246425576229652155786091497

a-invariants: [1, 0, 0, -10596063090767790103, 20246425576229652155786091497]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/10ℤ
conductor (N): 22176069865950
discriminant (Δ): -100944343291729053680130496829209274169579841372378497024000
Faltings height: 10.0207
naive height: 143.8787 ☆ record for ℤ/10ℤ torsion, rank ≥ 3
primes of bad reduction: 2, 3, 5, 7, 11, 13, 31, 61, 83, 941
regulator: 660.54176133636823545548056037558500604314791
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:26:19 UTC
last updated: 2026-09-25 00:26:19 UTC

Witness: 3 independent points log in to add more points →

(86557190806/225, 429925436799962459/3375)
(-153244167082/49, 51787867600222307/343)
(2982844086655766/1050625, 123008732639297532371989/1076890625)

Commentary

Torsion Z/10. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank Also found by Rathbun (2003) (see https://web.math.pmf.unizg.hr/~duje/tors/z10old3.html=

last edited by dujella at 2026-09-25 06:50:01 UTC · history