Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #1508

y² + xy + y = x³ + x² − 4866313x − 604174594

a-invariants: [1, 1, 1, -4866313, -604174594]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 402396225
discriminant (Δ): 7218671928935251640625
Faltings height: 2.8842
naive height: 57.8071
primes of bad reduction: 3, 5, 7, 11, 59, 1181
regulator: 55.45871644571928477734844920703480718897443513
submitted by: hdeping
submitted at: 2026-09-25 00:43:26 UTC
last updated: 2026-09-25 00:43:26 UTC

Witness: 4 independent points log in to add more points →

(19670, 2731452)
(-17906/9, 964975/27)
(-80470/49, 18948336/343)
(-8345/4, 182391/8)

Commentary

Specialization t=-649/245 of the Kubert-Tate torsion Z/4 universal family y^2+xy+ty=x^3+tx^2.

last edited by hdeping at 2026-09-27 08:27:02 UTC · history

Log in to edit commentary.