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curve #2131

y² + y = x³ + x² − 203x + 1048

a-invariants: [0, 1, 1, -203, 1048]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 973
discriminant (Δ): 973
Faltings height: -0.1370
naive height: 27.5581
primes of bad reduction: 7, 139
regulator: 5.219287663938723844539957496132985677011
submitted by: hdeping
submitted at: 2026-09-26 10:39:50 UTC
last updated: 2026-09-26 10:39:50 UTC

Witness: 1 independent point log in to add more points →

(74/25, 2682/125)

Commentary

Specialization of the torsion Z/3 family E: y^2+a*x*y+b^3*y=x^3, arising from x/y+y/z+z/x = k with k = 10.

last edited by hdeping at 2026-09-27 08:42:45 UTC · history

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